SOLUTION: Solve for x in the following eguation. 5=9^x-1 (as in x-1 are exponents.) I can't figure out where the log goes... :(

Question 71846: Solve for x in the following eguation.
5=9^x-1
(as in x-1 are exponents.)
I can't figure out where the log goes... :(
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The log of base 9 goes on both sides. The log undoes an exponent, so we use the log on the entire right side, but we must do it to both sides.

Take the log of both sides.The log simply cancels out the base 9
Add 1 to both sides
Since log_[9](5) is a number we can find x
Use the change of base formula
Where b is the base and x is the argument. Remember the base of the log is assumed to be 10 if not specified.
So this can be evaluated on a calculator

Check:

Which is close enough to 5 (there are some roundoff errors).
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