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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