Solving Exponential Equations using Logarithms

Example 1:

Solve for $x$ : $2^x=12$

      $\begin{array}{l}\log 2^x=\log 12\\ x\log 2=\log 12\\ x=\frac{\log 12}{\log 2}\approx 3.585\end{array}$

Example 2:

Solve for $x$ : $8\left({10}^x\right)=12$

      $\begin{array}{l}{10}^x=\frac{12}{8}=\frac{3}{2}\\ \log {10}^x=\log \frac{3}{2}\\ x\log 10=\log \frac{3}{2}\\ x=\log \frac{3}{2}\approx 0.176\end{array}$

Example 3:

Solve for $x$ : $e^{5x}=30$

      $\begin{array}{l}\ln e^{5x}=\ln 30\\ 5x\ln e=\ln 30\\ 5x=\ln 30\\ x=\frac{\ln 30}{5}\approx 0.680\end{array}$