# Logarithmic equations

To solve logarithmic equations it will be useful for you to remember these **basic properties of logarithms**:

To solve a basic logarithmic equation, only rewrite the equation in exponential form and solve for the variable.

Solve: log_{2}512 = -3x+9

512 = 2^{-3x+9} <=> 2^{9}= 2^{-3x+9} <=> 9=-3x+9 <=> 3x = 0 <=> x = 0

Solve: log_{4}(5x+6) = 4

5x+6=4^{4} <=> 5x+6=256 <=> 5x=250 <=> x=50