Question

Applying Inverse Properties In Exercise,apply the inverse properties of logarithmic and exponential functions to simplify the expression.See example 2.

- 1 + In e2x

Answer 1

2x - 1

Explanation:

Since logarithm has the following property:

If
`f(x)=b^x` and
`g(x)=\log_bx`,

Then
`fog=b^(\log_bx)=x` and
`gof=\log_bbx=x`

Therefore,

`- 1 + \ln e^(2x) = - 1 + \log_e e^(2x) = 2x-1`