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)   (Show Source): You can put this solution on YOUR website!
not sure if missing grouping symbols but in case






Computes to about 0.7854
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
8^x-2 = 2/25, find x
~~~~~~~~~~~~~~~~~


            Simpler solution is possible. 


Your starting equation is


     = .


It is equivalent to


     = .


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 = - 

     3x     = -  + 9

      x     = -  + 3 = 0.785381  (approximately; rounded).    ANSWER


CHECK.  The left side of the original equation is   = 0.080000 =  = .    ! Correct !

Solved.



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

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


 

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