SOLUTION: Solve for x: log 2,(log 5,(x-1)) = 1 Thank you for your help! I appreciate it!

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Question 354512: Solve for x:
log 2,(log 5,(x-1)) = 1
Thank you for your help!
I appreciate it!
Answer by jsmallt9(3296) About Me  (Show Source):
You can put this solution on YOUR website!
log%282%2C%28log%285%2C%28x-1%29%29%29%29+=+1
For an equation of this form, log(expression) = expression, and the variable in the argument of the log, you want to rewrite the equation in exponential form. In general log%28a%2C+%28p%29%29+=+q is equivalent to a%5Eq+=+p. So your equation is equivalent to:
2%5E1+=+log%285%2C+%28x-1%29%29
which simplifies to:
2+=+log%285%2C+%28x-1%29%29
We still have an equation of the form, log(expression) = expression, so we will repeat the procedure of rewriting it in exponential form:
5%5E2+=+x-1
which simplifies to:
25+=+x-1
Solving this simple equation gives us:
26+=+x