Exponential inequalities

In exponential inequalities too one “removes the base”, but with an extra caution: the direction of the inequality is preserved if $a>1$ and reversed if $0<a<1$. Forgetting the change of direction is the most frequent mistake. The section establishes the rule, illustrates it with many guided examples with base less than $1$ and warns against the two trivial cases in which the exponential is always positive.

• The rule of the direction
• Guided examples with base less than 1
• The trivial cases of the positive exponential