Here, b= 10, x= 4, and [latex]y=\frac{1}{10,000}\\[/latex]. The solution \(\ln(7)\) is not a real number, and in the real number system this solution is rejected as an extraneous solution. The given exponential form is \(3^7 = 2187\). Example 1: Given that \(3^7 = 2187\). Convert to exponential form. y = logb(x) is equivalent to by = x for x > 0, b > 0, b 1. Example 7 : Obtain the equivalent logarithmic form of the following. 1, 2.5, 6.3, 9.8) and n is an integer (e.g. 0.1 = 10-1 Solution : Given . 1/144 = 12-2. Four examples are worked out. log28 = 3. If one of the terms in the equation has base 10, use the common logarithm. Worksheet 1.8 Power Laws www.yumpu.com. Convert the given exponential to log form. Introduction to Transformation of Functions, 91. Use the one-to-one property to set the arguments equal. Combine vertical and horizontal shifts, 98. An exponential function is defined as- where a is a positive real number, not equal to 1. Solve Logarithmic Equations By Converting To Exponential Form - YouTube www.youtube.com. Use polynomial division to solve application problems, 140. Exponential to Log To convert exponential form to logarithmic form, identify the base of the exponential equation and then move base to the other side of the equal sign and add the word "log". We can solve exponential equations with base \(e\), by applying the natural logarithm of both sides and then using the fact that \( \ln (e^U) = U \). The exponentials are helpful to easily represent large algebraic expressions. Properties Of Logarithms Worksheet Answers - Properties Of Logarithms lorenxiorset.blogspot.com. How would we solve forx? An example of an exponential form number would be that in order to show 3x3x3x3, we'd instead write 34. \end{align*}\]. Does every logarithmic equation have a solution? Example \(\PageIndex{2}\): Solve Equations by Rewriting Them to Have a Common Base, \[\begin{align*} 8^{x+2}&= {16}^{x+1}\\ {(2^3)}^{x+2}&= {(2^4)}^{x+1} \qquad&&\text{Write 8 and 16 as powers of 2}\\ 2^{3x+6}&= 2^{4x+4} \qquad&&\text{To take a power of a power, multiply exponents}\\ 3x+6&= 4x+4 \qquad&&\text{Use the one-to-one property to set the exponents equal}\\ x&= 2 \qquad&&\text{Solve for } x\end{align*}\], \[\begin{align*} 2^{5x}&= 2^{\frac{1}{2}} \qquad&&\text{Write the square root of 2 as a power of 2}\\ 5x&= \dfrac{1}{2} \qquad&&\text{Use the one-to-one property}\\ x&= \dfrac{1}{10} \qquad&&\text{Solve for } x \end{align*}\]. Use synthetic division to divide polynomials, 137. x\ln5+2\ln5&= x\ln4 \qquad&&\text{Use the distributive law}\\ Observe that the graph abovepasses the horizontal line test. It is important to remember that, although parts of each of the two graphs seem to lie on the x -axis, they are really a tiny distance above the x -axis. In calculations involving huge scientific and astronomical calculations, the exponential form is transformed to logarithmic form for easy calculations. Logarithmic Form to Exponential Form - onlinemath4all log 9 3 = 1/2. The solution \(1\) is negative, but it checks when substituted into the original equation because the argument of the logarithm functions is still positive. This alternative approach uses exponent properties instead. e^x&= 8 \\ logcd = a. Find the inverse of a polynomial function, 162. Convert from logarithmic to exponential form. [latex]{\mathrm{log}}_{b}\left(x\right)=y\Leftrightarrow {b}^{y}=x,\text{}b>0,b\ne 1[/latex], [latex]y={\mathrm{log}}_{b}\left(x\right)\text{ is equivalent to }{b}^{y}=x[/latex], http://cnx.org/contents/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175, we read [latex]{\mathrm{log}}_{b}\left(x\right)[/latex] as, the logarithm with base. Solving Systems of Equations by Graphing, 216. Use the rules of logarithms to combine like terms, if necessary, so that the resulting equation has the form \({\log}_bS={\log}_bT\). When asked how many times we'll need to multiply 2 in order to get 16, the answer is logarithm 4. \end{align*}\]. In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Determine whether a function is even, odd, or neither from its graph, 94. Identifying and Expressing Solutions to Systems of Equations, 219. Introduction to Exponential Functions, 167. Any exponential equation of the form ab=c can be written in logarithmic form using loga(c)=b. The exponential form \(a^x = N\) is transformed and written in logarithmic form as \(Log_aN = x\). Recall that we can write logarithmic functions in two different, but equivalent, forms: exponential form and logarithmic form (recall the detailed definitions here).So, it is important to know how to switch between these two forms as it will be helpful when solving equations or when graphing logarithmic functions. Graph exponential functions using transformations, 177. Example \(\PageIndex{6}\): Solve an Equation of the Form \(y = Ae^{kt}\), \[\begin{align*} 100&= 20e^{2t}\\ 5&= e^{2t} \qquad&&\text{Divide by the coefficient of the power}\\ \ln5&= 2t \qquad&&\text{Take ln of both sides. [latex]{\mathrm{log}}_{10}\left(1,000,000\right)=6[/latex], b. 5^{x+2}&= 4^x \qquad&&\text{Use the Exponent Product Rule in reverse}\\ Example 2: Converting from Exponential Form to Logarithmic Form Write the following exponential equations in logarithmic form. The base blogarithm of a number is the exponent by which we must raise bto get that number. Determining Whether Graphs of Lines are Parallel or Perpendicular, 26. x&=\dfrac{\ln \left (\dfrac{1}{25} \right )}{\ln \left (\dfrac{5}{4} \right )} \qquad&&\text{Divide by the coefficient of x} Introduction to Inverses and Radical Functions, 161. In order to analyze the magnitude of earthquakes or compare the magnitudes of two different earthquakes, we need to be able to convert between logarithmic and exponential form. Solving Quadratic Equations by Factoring, 45. Introduction: Other Types of Equations, 46. Choose an appropriate model for data, 214. First, identify the values of b, y, and x. In order to solve equations that contain exponentials, we need logarithmic functions. Logarithmic properties are helpful to work across complex logarithmic expressions. When given an equation of the form \({\log}_b(S)=c\), where \(S\) is an algebraic expression, we can use the definition of a logarithm to rewrite the equation as the equivalent exponential equation \(b^c=S\), and solve for the unknown. This means [latex]y={\mathrm{log}}_{b}\left(x\right)[/latex] and [latex]y={b}^{x}[/latex] are inverse functions. The exponential form is converted to logarithmic form and is further converted back using antilogs. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. How to: Given an equation containing logarithms, solve it using the one-to-one property, Example \(\PageIndex{12}\): Use the One-to-One Property of Logarithms to Solve an Equation, \[\begin{align*} \ln(x^2)&= \ln(2x+3)\\ x^2&= 2x+3 \qquad&&\text{Use the one-to-one property of the logarithm}\\ x^2-2x-3&= 0 \qquad&&\text{Get zero on one side before factoring}\\ (x-3)(x+1)&= 0 \qquad&&\text{Factor using FOIL}\\ The isolated value is the exponent on the base. Functions And Their Inverses - Worked Examples www.math.toronto.edu. The exponent form of a to the exponent of x is equal to N, which on converting to logarithmic form we have log of N to the base of a is equal to x. 25 &= \left(\frac{4}{5}\right)^x\qquad&&\text{Rewrite as a log equation}\\ Convert from exponential to logarithmic form, 185. We can also say, " b raised to the power of y is x ," because logs are exponents. The exponential form of a to the exponent of x is N, which is transformed such that the logarithm of N to the base of a is equal to x. we read [latex]{\mathrm{log}}_{b}\left(x\right)[/latex] as, the logarithm with base. logarithm logarithms single form sheet expanded expansion worksheets each rewrite rule quotient power expression mathworksheets4kids . The. 03:18 . After solving an exponential equation, check each solution in the original equation to find and eliminate any extraneous solutions (Specifically, \(b^p\) is ALWAYS positive). Observe that the graph abovepasses the horizontal line test. Find the input and output values of a function, 63. We can express the relationship between logarithmic form and its corresponding exponential form as follows: [latex]{\mathrm{log}}_{b}\left(x\right)=y\Leftrightarrow {b}^{y}=x,\text{}b>0,b\ne 1[/latex]. We read this as log base 2 of 32 is 5.. 3^2 >0 \text{ and } 2(3)+3 > 0 \color{Cerulean}{} \quad & \quad (-1)^2 > 0 \text{ and } 2(-1)+3 > 0 \color{Cerulean}{} && \text{Check the solution when substituted in the arguments is }> 0 Therefore, the equation [latex]{\mathrm{log}}_{6}\left(\sqrt{6}\right)=\frac{1}{2}[/latex] is equal to [latex]{6}^{\frac{1}{2}}=\sqrt{6}[/latex]. Because a logarithm is a function, it is most correctly written as [latex]{\mathrm{log}}_{b}\left(x\right)[/latex] using parentheses to denote function evaluation just as we would with [latex]f\left(x\right)[/latex]. An example is the function that . We reject the equation \(e^x=7\) because a positive number never equals a negative number. log2 logarithms log3. Use the fact that } ln(x) \text{ and } e^x \text{ are inverse functions}\\ t&= \dfrac{\ln5}{2} \qquad&&\text{Divide by the coefficient of t} \end{align*}\]. Solution 2x 1 = 22x 4 The common base is 2 x 1 = 2x 4 By the one-to-one property the exponents must be equal x = 3 Solve for x Try It 4.6.1 Solve 52x = 53x + 2. the domain of the logarithm function with base [latex]b \text{ is} \left(0,\infty \right)[/latex]. Exponential to log form is easy for calculations with the help of exponent formulas and logarithm formulas. The logarithmic form and antilog form requires the use of logarithmic tables for calculation. Become a problem-solving champ using logic, not rules. Therefore. Graph the functions listed in the library of functions, 69. Remember a logarithm is an exponent ! Here, b= 10, x= 4, and [latex]y=\frac{1}{10,000}[/latex]. Problem 2 : log 7 7 = 1. Keep in mind that the inverse of a function effectively undoes what the other does. To solve this equation, we can use the rules of logarithms to rewrite the left side as a single logarithm, and then apply the one-to-one property to solve for \(x\): \[\begin{align*} \log(3x-2)-\log(2)&= \log(x+4)\\ \log \left (\dfrac{3x-2}{2} \right )&= \log(x+4) \qquad&&\text{Apply the quotient rule of logarithms}\\ \dfrac{3x-2}{2}&= x+4 \qquad&&\text{Apply the one to one property of a logarithm}\\ 3x-2&= 2x+8 \qquad&&\text{Multiply both sides of the equation by 2}\\ x&= 10 \qquad&&\text{Subtract 2x and add 2} \end{align*}\]. The logarithmic form logaN = x l o g a N = x can be easily transformed into exponential form as ax = N a x = N. Then we write [latex]x={\mathrm{log}}_{b}\left(y\right)[/latex]. 23 = 8 2 3 = 8 52 = 25 5 2 = 25 x =. Finding the Sum and Difference of Two Matrices, 235. [latex]{\mathrm{log}}_{5}\left(25\right)=2[/latex], a. Solve. Note that many calculators require parentheses around the x. In this section, we will learn techniques for solving exponential functions. The exponential form ax = N a x = N is transformed and written in logarithmic form as LogaN = x L o g a N = x. x &= \dfrac{\ln 25}{\ln \ce{4/5}}\approx-14.4251 No. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. Introduction to Graphs of Linear Functions, 121. How to: Given an exponential equation with unlike bases, use the one-to-one property to solve it. Similarly, the operation of division is transformed into the difference of the logarithms of the two numbers. Certified minuteman press business cards view . For example, the logarithmic form of 23 = 8 is log2 (8) = 3. Find domains and ranges of the toolkit functions, 76. \qquad e^x-8&= 0 \\ In these cases, we simply rewrite the terms in the equation as powers with a common base, and solve using the one-to-one property. Then we write [latex]x={\mathrm{log}}_{b}\left(y\right)\\[/latex]. The equation that represents this problem is [latex]{10}^{x}=500[/latex], where xrepresents the difference in magnitudes on the Richter Scale. First, identify the values of b,y, andx. the range of the logarithm function with base [latex]b \text{ is} \left(-\infty ,\infty \right)[/latex]. We read this as log base 2 of 32 is 5.. Introduction: Matrices and Matrix Operations, 234. In the example of , , and . Let us look at the following important formulas of logarithms. Given the equations of two lines, determine whether their graphs are parallel or perpendicular, 123. Question: Write the logarithmic equation in exponential form. Introduction to Dividing Polynomials, 135. Logarithmic form Logarithms are inverses of exponential functions. Then, write the equation in the form [latex]x={\mathrm{log}}_{b}\left(y\right)[/latex]. Solving Systems of Equations in Two Variables by the Addition Method, 218. And it's as simple as that. We identify the base b, exponent x, and output y. Keep in mind that we can only apply the logarithm to a positive number. For any algebraic expressions \(S\) and \(T\), and any positive real number \(b1\), \[\begin{align} b^S=b^T\text{ if and only if } S=T \end{align}\]. \({\log}_bS={\log}_bT\) if and only if \(S=T\). This equation has no solution. We read a logarithmic expression as, The logarithm with base bof xis equal to y, or, simplified, log base bof xis y. We can also say, braised to the power of yis x, because logs are exponents. Also, we cannot take the logarithm of zero. Understanding what a logarithm is requires understanding what an exponent is. e^x&= -7\\ The exponential function [latex]y={b}^{x}[/latex] is one-to-one, so its inverse, [latex]x={b}^{y}[/latex] is also a function. Introduction to Systems of Linear Equations: Three Variables, 223. Introduction to Solving Systems with Cramer's Rule, 251. Therefore, the equation [latex]{2}^{3}=8[/latex] is equivalent to [latex]{\mathrm{log}}_{2}\left(8\right)=3[/latex]. Write the following exponential equations in logarithmic form. For example, the base 2 logarithm of 32 is 5, because 5 is the exponent we must apply to 2 to get 32. e^{2x}-e^x-56&= 0 \qquad&&\text{Get one side of the equation equal to zero}\\ An example of an equation with this form that does not have a solution is \(2=3e^t\), which would mean \(e^t\) is negative, which is impossible. Identify the base, answer of the exponential and exponent. Introduction to Systems of Nonlinear Equations and Inequalities: Two Variables, 228. Then we write x = logb(y) x = l o g b ( y). We want to calculate the difference in magnitude. logarithms. 5^x \cdot25 &= 4^x \qquad&&\text{ }\\ exponential logarithmic form worksheet pdf answers printable. Use the quotient and power rules for logarithms, 196. How to: Given an equation of the form \(y=Ae^{kt}\), solve for \(t\). Determine whether a relation represents a function, 62. log 9 3 = 1/2. To find an algebraic solution, we must introduce a new function. The solution is \(x = 0\). Therefore, the equation [latex]{10}^{-4}=\frac{1}{10,000}[/latex] is equivalent to [latex]{\text{log}}_{10}\left(\frac{1}{10,000}\right)=-4[/latex]. One such situation arises in solving when the logarithm is taken on both sides of the equation. Solve the resulting equation, \(S=T\), for the unknown. {eq}\log_2 64 = 6 {/eq} The logarithm value of 6 identifies an. First, identify the values of b, y, and x. Evaluate a polynomial using the Remainder Theorem, 142. However, when the input is a single variable or number, it is common to see the parentheses dropped and the expression written without parentheses, as [latex]{\mathrm{log}}_{b}x[/latex]. No. Solution: Step 1: Set up the equation and use the definition to change it. Here, [latex]b=6,y=\frac{1}{2},\text{and } x=\sqrt{6}[/latex]. Therefore, we can solve many exponential equations by using the rules of exponents to rewrite each side as a power with the same base. Base: 5, Answer of exponential: 625, exponent: x. x =. Estimating from a graph, however, is imprecise. This video defines a logarithms and provides examples of how to convert between exponential equations and logarithmic equations. 6-2 = 1 36 Evaluate the function at the indicated value of x without . If the base is e (euler's number), rather than writing log e, it gets its own symbol as ln (read as "lawn"). Using logarithm rules, this answer can be rewrittenin the form \(t=\ln\sqrt{5}\). 5^{x+2}&= 4^x \qquad&&\text{There is no easy way to get the powers to have the same base}\\ Graphing Nonlinear Inequalities and Systems of Nonlinear Inequalities, 233. Polynomial and Rational Functions Practice Test, 8. Because the base of an exponential function is always positive, no power of that base can ever be negative. For any algebraic expression \(S\) and real numbers \(b\) and \(c\), where \(b>0\), \(b1\), \[\begin{align} {\log}_b(S)=c \text{ if and only if } b^c=S \end{align}\], Example \(\PageIndex{10}\): Rewrite a Logarithmic Equation in Exponential Form, \[\begin{align*} 2\ln x+3&= 7\\ 2\ln x&= 4 \qquad&&\text{Subtract 3}\\ \ln x&= 2 \qquad&&\text{Divide by 2}\\ x&= e^2 \qquad&&\text{Rewrite in exponential form} \end{align*}\], \[\begin{align*} 2\ln(6x)&= 7\\ \ln(6x)&= \dfrac{7}{2} \qquad&&\text{Divide by 2}\\ 6x&= e^{\left (\dfrac{7}{2} \right )} \qquad&&\text{Use the definition of }\ln \\ x&= \tfrac{1}{6}e^{\left (\tfrac{7}{2} \right )} &&\qquad \text{Divide by 6} \end{align*}\]. Use the Factor Theorem to solve a polynomial equation, 143. We read logb(x) as "log base b of x ." It is equivalent to saying "the exponent on b to get x ." Exponential form : 1 = 5 0. When \(k0\), there is a solution when \(y\) and \(A\) are either both 0, or when neither is 0and they have the same sign. If it is not, it must be rejected as a solution. By equating it with the formula given above, we can say that, here, b = 125, a = 3, and e = 5. The exponential form of a to the exponent of x is N, which is transformed such that the logarithm of N to the base of a is equal to x. Therefore, the equation [latex]{10}^{-4}=\frac{1}{10,000}\\[/latex] is equivalent to [latex]{\text{log}}_{10}\left(\frac{1}{10,000}\right)=-4\\[/latex]. First, identify the values of b,y, andx. When we plan to use factoring to solve a problem, we always get zero on one side of the equation, because zero has the unique property that when a product is zero, one or both of the factors must be zero. Exponential to log form is a common means of converting one form of a mathematical expression to another form. The basic formula of exponents is ap = a a a a a a .. p times, and the formulas of logarithms is Logab = Loga + Logb, and Loga/b = Loga - Logb. Write the following exponential equations in logarithmic form. Rewrite [latex]{\mathrm{log}}_{b}x=y[/latex] as [latex]{b}^{y}=x[/latex]. Setting up a Linear Equation to Solve a Real-World Application, 28. Introduction to Rates of Change and Behaviors of Graphs, 77. The logarithmic to exponential form on conversion is equal to \(7^3 = 343\). Restrict the domain to find the inverse of a polynomial function, 165. Logarithms Worksheets www.mathworksheets4kids.com. Introduction to Zeros of Polynomials, 141. Logarithmic Form Exponential Form (a) log 25 25 = 25 5= 2 (b) log 1000 310 = 1000 10= 3 (c) log 3.55 a = a =53.5 (d . A history note: common logarithms are also called Briggs' logarithms, after Henry Briggs (1561-1630). Find the domains of rational functions, 155. The exponential form is useful to combine and write a large expression of multiplication of the same number numerous times, into a simple formula. For example, the exponential equation 23=8 is written as log2(8)=3 in logarithmic form. \displaystyle {2}^ {3}=8 2 3 = 8 \displaystyle {5}^ {2}=25 5 2 = 25 Do not change anything but the base, the other numbers or variables will not change sides. \end{align*}\]. Download for free athttps://openstax.org/details/books/precalculus. None of the algebraic tools discussed so far is sufficient to solve [latex]{10}^{x}=500[/latex]. the domain of the logarithm function with base [latex]b \text{ is} \left(0,\infty \right)[/latex]. Write the following logarithmic equations in exponential form. Log to exponential form is useful to easily perform complicated numeric calculations. As is the case with all inverse functions, we simply interchange xand yand solve for yto find the inverse function. Introduction to Systems of Linear Equations: Two Variables, 215. For example, consider the equation \({\log}_2(2)+{\log}_2(3x5)=3\). Find the domain of a function defined by an equation, 70. Since [latex]{2}^{5}=32[/latex], we can write [latex]{\mathrm{log}}_{2}32=5[/latex]. When we are given an exponential equation where the bases are. the range of the logarithm function with base [latex]b \text{ is} \left(-\infty ,\infty \right)[/latex]. Then, write the equation in the form [latex]x={\mathrm{log}}_{b}\left(y\right)[/latex]. The exponential function [latex]y={b}^{x}[/latex] is one-to-one, so its inverse, [latex]x={b}^{y}[/latex] is also a function. The log form and exponential form are actually inverses of each other. The given logarithmic form is \(log_7343=3\). Also, we cannot take the logarithm of zero. Phone 201-782-9000 . Solving a System of Linear Equations Using Matrices, 245. For example, suppose the amount of energy released from one earthquake were 500 times greater than the amount of energy released from another. Example \(\PageIndex{8}\): Simplify using Exponent Rules before writing in Logarithmic form, \[\begin{align*} To convert from exponents to logarithms, we follow the same steps in reverse. Exponential functions are inverses of logarithmic functions. We have already seen that every logarithmic equation \({\log}_b(x)=y\) is equivalent to the exponential equation \(b^y=x\). Write the following exponential equations in logarithmic form. Here, b= 2, x= 3, and y= 8. Because Australia had few predators and ample food, the rabbit population exploded. Using a Formula to Solve a Real-World Application, 32. Since \displaystyle {2}^ {5}=32 25 = 32, we can write \displaystyle {\mathrm {log}}_ {2}32=5 log232 = 5. This reduces the complexity of calculations as it can be calculated in a few quick steps. Exponential to log form is useful for working across large calculations. It tells us how many times we'll need to multiply a number in order to get another number. Introduction to Solving Systems with Gaussian Elimination, 240. Examine the equation [latex]y={\mathrm{log}}_{b}x[/latex] and identify. 5^x \cdot5^2 &= 4^x \qquad&&\text{ }\\ In order to analyze the magnitude of earthquakes or compare the magnitudes of two different earthquakes, we need to be able to convert between logarithmic and exponential form. Introduction to Graphs of Exponential Functions, 174. We can examine a graphto better estimate the solution. Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here. Confirm that each solution is correct. Always check for extraneous solutions. The above formula gives a general representation and conversion from exponential to log form. Rearrange if necessary. Identify the domain of a logarithmic function, 188. (x+2)\ln5&= x\ln4 \qquad&&\text{Power Rule for Logarithms}\\ To check the result, substitute \(x=10\) into \(\log(3x2)\log(2)=\log(x+4)\). Jay Abramson (Arizona State University) with contributing authors. Solving Systems of Equations by Substitution, 217. exponential. Write the equation for a linear function from the graph of a line, 122. MTH 165 College Algebra, MTH 175 Precalculus, { "4.6e:_Exercises_-_Exponential_and_Logarithmic_Equations" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass226_0.b__1]()" }, { "4.01:_Exponential_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass226_0.b__1]()", "4.02:_Graphs_of_Exponential_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass226_0.b__1]()", "4.03:_Logarithmic_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass226_0.b__1]()", "4.04:_Graphs_of_Logarithmic_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass226_0.b__1]()", "4.05:_Logarithmic_Properties" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass226_0.b__1]()", "4.06:_Exponential_and_Logarithmic_Equations" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass226_0.b__1]()", "4.07:_Exponential_and_Logarithmic_Models" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass226_0.b__1]()" }, { "00:_Front_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass226_0.b__1]()", "00:_Preliminary_Topics_for_College_Algebra" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass226_0.b__1]()", "01:_Equations_and_Inequalities" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass226_0.b__1]()", "02:_Functions_and_Their_Graphs" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass226_0.b__1]()", "03:_Polynomial_and_Rational_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass226_0.b__1]()", "04:_Exponential_and_Logarithmic_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass226_0.b__1]()", "05:_Trigonometric_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass226_0.b__1]()", "06:_Periodic_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass226_0.b__1]()", "07:_Trigonometric_Identities_and_Equations" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass226_0.b__1]()", "08:_Further_Applications_of_Trigonometry" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass226_0.b__1]()", "zz:_Back_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass226_0.b__1]()" }, 4.6: Exponential and Logarithmic Equations, [ "article:topic", "one-to-one property for exponential functions", "definition of a logarithm", "one-to-one property for logarithmic functions", "license:ccby", "showtoc:yes", "source-math-1357", "source[1]-math-1357" ], https://math.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fmath.libretexts.org%2FCourses%2FMonroe_Community_College%2FMTH_165_College_Algebra_MTH_175_Precalculus%2F04%253A_Exponential_and_Logarithmic_Functions%2F4.06%253A_Exponential_and_Logarithmic_Equations, \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\), 4.5e: Exercises - Properties of Logarithms, 4.6e: Exercises - Exponential and Logarithmic Equations, Use the One-to-One Property of Exponential Functions, Exponential Equations that are quadratic in form, Use the One-to-One Property of Logarithms, https://openstax.org/details/books/precalculus, one-to-one property for exponential functions, one-to-one property for logarithmic functions, status page at https://status.libretexts.org, One-to-one property for exponential functions. Introduction to Linear Equations in One Variable, 20. We have not yet learned a method for solving exponential equations.