math

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solve the equation.

log2(x+4)-log4x=2

please show work

  • math -

    we should have the same base in the logs

    let log4x = y
    then 4^y = x
    2^(2y) = x
    log2 x = 2y
    y = (1/2)log2 x
    = log2 x^(1/2)
    = log2√x

    then log4x = log2 √x

    log2[ (x+4)/√x] = 2

    (x+4)/√x = 2^2 = 4
    x+4 = 4√x
    square both sides
    x^2 + 8x + 16 = 16x
    x^2 - 8x + 16 = 0
    (x-4)^2 = 0
    x-4 = 0

    x = 4

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