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Math Help - help solving logarithms

  1. #1
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    help solving logarithms

    stuck with this one

    solve for x: 16^x-5*8^x=0
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  2. #2
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    Re: help solving logarithms

    Quote Originally Posted by calmo11 View Post
    stuck with this one

    solve for x: 16^x-5*8^x=0
    $16^x-5*8^x=0$

    $16^x = 5*8^x$

    take logs base 2

    $4x=3x+\log_2(5)$

    $x = \log_2(5)$
    Thanks from calmo11
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  3. #3
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    Re: help solving logarithms

    Or for log to any base, x log(16)= log(5)+ x log(8) so x(log(16)- log(8))= x(log(16/8))= x(log(2))= log(5) and x= log(5)/log(2).

    Another way to do this is, since [tex]8^x[/itex] is never 0, to divide both sides by 8^x:
    \frac{16^x}{8^x}= \left(\frac{16}{8}\right)^x= 2^x= 5
    and then log(2^x)= xlog(2)= log(5) so x= \frac{log(5)}{log(2)}
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