# How do you evaluate #ln(ln e^(e^100))#?

##### 2 Answers

Mar 31, 2016

100

#### Explanation:

The bracketed logarithm

The given expression =

Apr 5, 2016

#### Explanation:

We have:

#ln(ln(e^(e^100)))#

Within the innermost logarithm, we can use the following rule:

#ln(color(blue)a^color(red)b)=color(red)b*ln(color(blue)a)#

This gives us:

#ln(ln(color(blue)e^(color(red)(e^100))))=ln(color(red)(e^100)*ln(color(blue)(e)))#

Since

#ln(e^100*ln(e))=ln(e^100)#

Using the previously defined exponent rule, we can rewrite this as follows:

#ln(color(blue)e^color(red)100)=color(red)100*ln(color(blue)e)=barul|color(white)(a/a)100color(white)(a/a)|#