SOLUTION: Show all work for the following problems. Give exact answers. a.) log(log(googol)) = ? b.) log(log(log(googolplex))) = ?

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Question 1129947: Show all work for the following problems. Give exact answers.
a.) log(log(googol)) = ?
b.) log(log(log(googolplex))) = ?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
a.
A googol is 10%5E100
log%28%28log%28%28googol%29%29%29%29+
=log%28%28log%28%2810%5E100%29%29%29%29++
=log%28%28100%2Alog%28%2810%29%29%29%29+
=log%28%28100%2A1%29%29+
=log%28%2810%5E2%29%29

=2log%28%2810%29%29

=2%2A1
=2

b.

and a googolplex is 10%5Egoogol: 10%5E%2810%5E100%29

log%28%28log%28%28log%28%2810%5E%2810%5E100%29%29%29%29%29%29%29
=log%28%28log%28%2810%5E100%2Alog%2810%29%29%29%29%29
=log%28%28log%28%2810%5E100%2A1%29%29%29%29
=log%28%28100%2Alog%28%2810%29%29%29%29
=log%28%28100%29%29
=log%28%2810%5E2%29%29+
=2log%28%2810%29%29

=2%2A1
=2