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March 28, 2017

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log4x^4 + log4^2 = 3

Solve the logarithmic equation.

  • Math - ,

    log4x^4 = log4 + 4logx
    log4^2 = 2log4

    log4 + 4logx + 2log4 = 3
    3log4 + 4logx = 3
    4logx = 3(1-log4)

    Now, if we're dealing with base 10, 1 = log10, so 1-log4 = log(10/4) = log(5/2)

    4 logx = 3log(5/2)
    logx = 3/4 log(5/2)

    x = 10^(3/4) * l0^(log 5/2)
    x = 10^3/4 * 5/2
    x = 5/2 10^(3/4)
    x = 5/2 ∜1000

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