SOLUTION: If log7(log3(log2(x)))=0, find the value of x^-1/2.

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Question 959136: If log7(log3(log2(x)))=0, find the value of x^-1/2.
Found 2 solutions by Fombitz, jsmallt9:
Answer by Fombitz(32388) About Me  (Show Source):
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
First we will find x and then x^(-1/2). To find x we will repeatedly rewrite the equation in exponential form (to "peel away" the logs).

In general log%28a%2C+%28p%29%29+=+n is equivalent to a%5En+=+p. Using this pattern on
log%287%2C+%28log%283%2C+%28log%282%2C+%28x%29%29%29%29%29%29=0
7%5E0+=+log%283%2C+%28log%282%2C+%28x%29%29%29%29%29%29
which simplifies to:
1+=+log%283%2C+%28log%282%2C+%28x%29%29%29%29%29%29
Repeating...
3%5E1+=+log%282%2C+%28x%29%29%29%29
3+=+log%282%2C+%28x%29%29%29%29
Again...
2%5E3+=+x
8+=+x

Now for x%5E%28-1%2F2%29:
8%5E%28-1%2F2%29
1%2F8%5E%281%2F2%29
1%2Fsqrt%288%29
%281%2Fsqrt%288%29%29%28sqrt%282%29%2Fsqrt%282%29%29
sqrt%282%29%2Fsqrt%2816%29
sqrt%282%29%2F4