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

2 Answers
Mar 31, 2016

Answer:

100

Explanation:

#ln (e^a)=a#
The bracketed logarithm #ln( (e)^(e^100))=e^100#
The given expression = #ln (e^100)# = 100.

Apr 5, 2016

Answer:

#100#

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)=1#, this equals

#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)|#