When solving exponential inequalities it is very important that you look at the value of the argument in the logarithm. That value determines whether you have to turn the inequality sign when you multiply or divide by or .
Rule
When , and you can solve the inequality as usual.
When , , you will have to turn the inequality sign as you end up dividing or multiplying by a negative number!
Example 1
Solve the inequality
Example 2
Solve the inequality
Example 3
Solve the inequality