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Math Help - Solving a log equation with two variables

  1. #1
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    Solving a log equation with two variables

    Blue represents the base of the log.
    Problem: (2a) (4a^2)^3 = x" alt="log (2a) (4a^2)^3 = x" />

    Attempted Solution: I converted the logarithm into exponential form.

    2a^x = (4a^2)^3
    2a^x = 64a^6
    2a^x/2 = 64a^6/2
    a^x = 32a^6

    I cannot see where to go from here.

    Could someone please help?
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by D. Martin View Post
    Blue represents the base of the log.
    Problem: (2a) (4a^2)^3 = x" alt="log (2a) (4a^2)^3 = x" />

    Attempted Solution: I converted the logarithm into exponential form.

    2a^x = (4a^2)^3
    2a^x = 64a^6
    2a^x/2 = 64a^6/2
    a^x = 32a^6

    I cannot see where to go from here.

    Could someone please help?
    Note that \log_{2a}\left[(4a^2)^3\right]=3\log_{2a}(4a^2)=3\log_{2a}\left[(2a)^2\right]=6\log_{2a}(2a)=6

    Thus, \color{red}\boxed{x=6}

    Does this make sense?
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