Logarithms

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Solve log4 x + log4(x-2)=log4(15)


I know how do the example in my book but I don't know what I'm doing wrong here.

log4 x + log4(x-2)=log4(15)
log4 [x + log4(x-2)]=log4(15)
(x^2 + x)=4
x^2 + x-4=0

  • Logarithms -

    I see two major errors

    1. from log A + log B = log (A x B)
    your second line should have been
    log4 [x(x-2)]=log4(15)

    then in your third line

    the right side should have been 15, not 4

    so

    x(x-2) = 15
    x^2 - 2x - 15 = 0
    (x-5)(x+2) = 0
    x = 5 or x = -2, but x+-2 does not work since you cannot take the log of a negative

    so x=5

  • Logarithms (CORRECTION) -

    should have been
    x-5)(x+3) = 0
    x = 5 or x = -3, but x=-3 does not work since you cannot take the log of a negative

    so x =l 5 is still the only solution

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