Exponential Functions

Solving Exponential Equations

An exponential equation is an equation in which one or more of the terms is an exponential function. e.g. $5^{x}=2^{x+2}$. Exponential equations can be solved with logarithms.

e.g. Solve $3^{x+1}=4^{2x-1}$

${\begin{aligned}3^{x+1}&=4^{2x-1}\\(x+1)\ln 3&=(2x-1)\ln 4\\x\ln 3+\ln 3&=2x\ln 4-\ln 4\\\ln 3+\ln 4&=x(2\ln 4-\ln 3)\\x&={\frac {\ln 3+\ln 4}{2\ln 4-\ln 3}}\\x&\approx 1.4844\end{aligned}}$

Resources

• Exponential Functions, Book Chapter
• Guided Notes