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 $3^{x+1}=4^{2x-1}$

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