Background (inverse property)

The inverse properties are often used in solving exponential and logarithmic equations. These properties are

1. for all x

2. for x > 0

Here are the two properties written in the special case when the base is e.

1. for all x

2. for x > 0

Since we have used the first property before, we will illustrate the second one.

When a =2 and x = 32, this property says that Let's check this by going through the left side step by step. Noting that , we get

= = 32 as predicted.