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Math

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Solve
log10(8 x) − log10(1 + √x) = 2
for x.

  • Math -

    the 10s were supposed to be subscripts so just ignore them

  • Math -

    If the 10's are subscripts, they are meant to be the base of the log, and are important.

    log10(8 x) − log10(1 + √x) = 2
    log10(8x/(1+√x)) = 2
    Take anti-log (or raise to power of 10)
    8x/(1+√x) = 10²
    8x=100(1+√x)
    If you plot the graph 8x-100(1+√(x)), you will find a minimum of about -400 at x=40, and a zero at about x=180.4.

  • Math -

    log( 8x/(1+√x) = 2
    8x/(1+√x) = 100
    8x = 100 + 100√x
    8x - 100 = 100√x
    square both sides
    64x^2 - 1600x + 10000 = 10000x
    64x^2 - 11600x + 10 000 = 0

    x = (11600 ± √132000000)/128
    = 180.384 or .8662

    since we squared we must check the answer
    1. x = 180.384
    LS = 2
    RS = 2

    2. x = .8662
    LS = .555 ≠ RS

    so x = 180.384

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