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Let 2^a = 5 and 2^b = 3. Using exponent rules, solve the equation in terms of a and b.
0.4^x = 27

  • math -

    27 = .4^x
    3^3 = .4^x
    (2^b)^3 = .4^x
    2^(3b) = (2/5)^x
    2^(3b) = (2/(2^a))^x
    2^(3b) = 2^x / 2^(ax)
    2^(3b) 2^(ax) = 2^x
    2^(3b+ax) = 2^x

    3b + ax = x
    x-ax = 3b
    x(1-a) = 3b
    x = 3b/(1-a)

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