SOLUTION: Solve the following equation for x:(1/8)^x=25 Thanks!

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Question 730282: Solve the following equation for x:(1/8)^x=25
Thanks!
Found 2 solutions by lynnlo, ikleyn:
Answer by lynnlo(4176) About Me  (Show Source):
Answer by ikleyn(53341) About Me  (Show Source):
You can put this solution on YOUR website!
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Solve the following equation for x: (1/8)^x=25
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Your starting equation is

    %281%2F8%29%5Ex = 25.


It is the same as

    2%5E%28-3x%29 = 25.


Multiply both sides by 4.  You will get an equivalent equation

    2%5E%282-3x%29 = 100.


Take logarithm base 2 of both sides

    2 - 3x = log%282%2C%28100%29%29,

    2 - 3x = 2%2Alog%282%2C%2810%29%29,

    2+-+2%2Alog%282%2C%2810%29%29 = 3x,

    x = %282+-+2%2Alog%282%2C%2810%29%29%29%2F3 = -1.547952063...


ANSWER.  x = -1.547952, approximately.


CHECK.  %281%2F8%29%5E%28-1.547952063%29 = 24.9999999866,  which is good match.

Solved.