SOLUTION: Solve for x: 32^x = 8^2x-1

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Question 978393: Solve for x: 32^x = 8^2x-1
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!


No logarithms are needed, although you can get the answer
with logs.  But I won't use logs here:

Write 32 as 25 and 8 as 23



Remove the parentheses by multiplying the exponents:



The bases are equal, non-negative and not equal to 1, so
the exponents are equal, so we can drop the bases:



You finish.

Edwin
Answer by ikleyn(52832)   (Show Source): You can put this solution on YOUR website!

As I understand,  you need to solve an equation

= ,

correct?

If so,  then let us transform this equation step by step.
Since   =   and   = ,  we have

= .

It implies that

5x = 3*(2x - 1).

Solve this equation simplifying it step by step:

5x = 6x - 3,
-x = -3,
x = 3.

Check yourself the solution  x = 3.

Answer.  x = 3.


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