Difference between revisions of "Exponential Functions"

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== Solving Exponential Equations ==
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An '''exponential equation''' is an equation in which one or more of the terms is an exponential function. e.g. <math>5^x = 2^{x+2}</math>. Exponential equations can be solved with logarithms.
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e.g. Solve <math>3^{x+1} = 4^{2x-1}</math>
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<math>\begin{align}
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3^{x+1} &= 4^{2x-1} \\
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(x+1)\ln 3 &= (2x-1)\ln 4 \\
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x\ln 3 + \ln 3 &= 2x\ln 4 - \ln 4 \\
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\ln 3 + \ln 4 &= x(2\ln 4 - \ln 3) \\
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x &= \frac{\ln 3 + \ln 4}{2\ln 4 - \ln 3} \\
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x &\approx 1.4844
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\end{align}</math>
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==Resources==
 
==Resources==
 
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Exponential%20Functions/MAT1053_M5.1Exponential_Functions.pdf Exponential Functions], Book Chapter
 
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Exponential%20Functions/MAT1053_M5.1Exponential_Functions.pdf Exponential Functions], Book Chapter
 
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Exponential%20Functions/MAT1053_M5.1Exponential_FunctionsGN.pdf Guided Notes]
 
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Exponential%20Functions/MAT1053_M5.1Exponential_FunctionsGN.pdf Guided Notes]

Revision as of 11:54, 4 October 2021

Solving Exponential Equations

An exponential equation is an equation in which one or more of the terms is an exponential function. e.g. . Exponential equations can be solved with logarithms.

e.g. Solve

Resources