SOLUTION: evaluate the expression log base 4 (log base 3 81) looks like log4(log3 81)

Question 539106: evaluate the expression
log base 4 (log base 3 81)
looks like log4(log3 81)
Answer by Mathpassionate(25) (Show Source): You can put this solution on YOUR website!
evaluate the expression
log base 4 (log base 3 81)
looks like log4(log3 81)

log base 4 (log base 3 81)

We have to evaluate in two parts:

First (log base 3 81)

We know that 81 = 3^4, So

Log base 3 3^4

We know that Log base A of A^b = b*Log base A of A

So

Log base 3 3^4 = 4*Log base 3 of 3

4*Log base 3 of 3 = 4*1
4*Log base 3 of 3 = 4

Then (log base 3 81) = 4

Now, log base 4 (log base 3 81) = log base 4 (4)

Using the main property of Logarithms: Log base A of A = 1

log base 4 of (4) = 1

The answer is: log base 4 (log base 3 81) = 1

Any questions, please ask me.

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