Question 730282
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Solve the following equation for x: (1/8)^x=25
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<pre>
Your starting equation is

    {{{(1/8)^x}}} = 25.


It is the same as

    {{{2^(-3x)}}} = 25.


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

    {{{2^(2-3x)}}} = 100.


Take logarithm base 2 of both sides

    2 - 3x = {{{log(2,(100))}}},

    2 - 3x = {{{2*log(2,(10))}}},

    {{{2 - 2*log(2,(10))}}} = 3x,

    x = {{{(2 - 2*log(2,(10)))/3}}} = -1.547952063...


<U>ANSWER</U>.  x = -1.547952, approximately.


<U>CHECK</U>.  {{{(1/8)^(-1.547952063)}}} = 24.9999999866,  which is good match.
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Solved.