SOLUTION: solve: {{{log base x[log base 2(log base 3 of 9)]=2}}} Unfortunately I do not know how to put this without all the words. But this is a problem on one of my take home tests. I do

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: solve: {{{log base x[log base 2(log base 3 of 9)]=2}}} Unfortunately I do not know how to put this without all the words. But this is a problem on one of my take home tests. I do      Log On


   

Question 250018: solve:
log+base+x%5Blog+base+2%28log+base+3+of+9%29%5D=2
Unfortunately I do not know how to put this without all the words. But this is a problem on one of my take home tests. I dont understand how to solve because I get 3%5E2=9 for the log in the parentheses but now I don't knwo what to do?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
log+base+x%5Blog+base+2%28log+base+3+of+9%29%5D=2
----
log3(9) = 2 so your problem becomes:
log+base+x%5Blog+base+2%282%29%5D=2
---
log2(2) = 1 so your problem becomes:
logx(1) = 2
---
x^2 = 1
x^2-1 = 0
(x-1)(x+1) = 0
x = 1 or x=-1
But -1 cannot be the base of a log.
So x = 1 is the only solution.
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Cheers,
Stan H.