You can find the solution of a logarithmic equation
by applying an exponential function with base
on both sides.
From then follows .
Conditions are that and and .
A logarithmic inequality can be solved using graphs:
First you need to solve the corresponding equation .
Then you look at the graphs of and . Make sure you take into account the domain (and the vertical asymptote) of the logarithm.
You can read off the solution for the equation.
When equations are more complicated and involve several logarithms you will also need to apply the properties for adding and subtracting logarithms. Sometimes you may also need to change bases.