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. 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 5^x = 2^{x+2}} . Exponential equations can be solved with logarithms.
e.g. Solve
Resources
- Exponential Functions, Book Chapter
- Guided Notes
