# How do you simplify #ln e^(2x)#?

##### 3 Answers

#### Explanation:

As a Real valued function,

As a result, for any

This is the definition of the Real natural logarithm.

If

#e^(ln(e^t)) = e^t#

Since

#ln e^t = t#

In other words,

So if

#ln e^(2x) = 2x#

#### Explanation:

Using the property of logs:

#log(a^b) = b log a#

We can see that:

#ln(e^(2x))=2x ln e#

And since

#2xlne=2x#

#### Explanation:

The key realization here is that

which just leaves us with

Hope this helps!