SOLUTION: 8^x-2 = 2/25, find x

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Question 1183047: 8^x-2 = 2/25, find x
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
not sure if missing grouping symbols but in case 8%5E%28x-2%29=2%2F25


log%28%288%5E%28x-2%29%29%29=log%28%282%2F25%29%29
%28x-2%29log%28%282%5E3%29%29=log%28%282%29%29-log%28%285%5E2%29%29
x-2=%28log%28%282%29%29-2%2Alog%28%285%29%29%29%2F%283%2Alog%28%282%29%29%29
x=2%2B%28log%28%282%29%29-2%2Alog%28%285%29%29%29%2F%283%2Alog%28%282%29%29%29
Computes to about 0.7854

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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8^x-2 = 2/25, find x
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            Simpler solution is possible. 


Your starting equation is


    8%5E%28x-2%29 = 2%2F25.


It is equivalent to


    2%5E%283%2A%28x-2%29%29 = 8%2F100.


Take logarithm base 10 of both sides


    3*(x-2)*log(2) = 3*log(2) - 2


Simplify

    (3x - 6)*log(2) = 3*log(2) - 2

    (3x - 6 - 3)*log(2) = -2

    (3x - 9)*log(2) = -2

     3x - 9 = - 2%2Flog%28%282%29%29

     3x     = - 2%2Flog%28%282%29%29 + 9

      x     = - 2%2F%283%2Alog%28%282%29%29%29 + 3 = 0.785381  (approximately; rounded).    ANSWER


CHECK.  The left side of the original equation is  8%5E%280.785381-2%29 = 0.080000 = 8%2F100 = 2%2F25.    ! Correct !

Solved.



Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

8^x-2 = 2/25, find x