# Solving Logarithmic Equations

To solve a logarithmic equation:

$1\right)$ Rewrite the equation in exponential form .

$2\right)$ Solve for the variable .

Example 1:

Solve for $x$ : ${\mathrm{log}}_{3}x=4$

$\begin{array}{l}{3}^{4}=x\\ x=81\end{array}$

Example 2:

Solve for $x$ : $\mathrm{ln}x=3$

$\begin{array}{l}{e}^{3}=x\\ x\approx 20.086\end{array}$

Example 3:

Solve for $x$ : ${\mathrm{log}}_{10}\left(x-3\right)=2$

${10}^{2}=x-3$

$100=x-3$

$x=103$