Difference between revisions of "Exponential Functions"
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| + | == Solving Exponential Equations == | ||
| + | |||
| + | 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. | ||
| + | |||
| + | e.g. Solve <math>3^{x+1} = 4^{2x-1}</math> | ||
| + | |||
| + | <math>\begin{align} | ||
| + | 3^{x+1} &= 4^{2x-1} \\ | ||
| + | (x+1)\ln 3 &= (2x-1)\ln 4 \\ | ||
| + | x\ln 3 + \ln 3 &= 2x\ln 4 - \ln 4 \\ | ||
| + | \ln 3 + \ln 4 &= x(2\ln 4 - \ln 3) \\ | ||
| + | x &= \frac{\ln 3 + \ln 4}{2\ln 4 - \ln 3} \\ | ||
| + | x &\approx 1.4844 | ||
| + | \end{align}</math> | ||
| + | |||
==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
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{align} 3^{x+1} &= 4^{2x-1} \\ (x+1)\ln 3 &= (2x-1)\ln 4 \\ x\ln 3 + \ln 3 &= 2x\ln 4 - \ln 4 \\ \ln 3 + \ln 4 &= x(2\ln 4 - \ln 3) \\ x &= \frac{\ln 3 + \ln 4}{2\ln 4 - \ln 3} \\ x &\approx 1.4844 \end{align}}
Resources
- Exponential Functions, Book Chapter
- Guided Notes
