College Algebra

1. 2log8^x=log8(4x+12)

both log bases are 8. I have no clue what to do.

2. 1/2ln (x) -3 ln y - ln (z-2)

so far for this second one i have

ln sqrt(x)-ln y^3 - ln (z-2)

dont know what to do next

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  1. #1.
    assuming base 8, just for ease of readability,

    2logx = log(4x+12)
    log(x^2) = log(4x+12)
    so, if the logs are equal, so are the numbers:
    x^2 = 4x+12
    x^2-4x-12=0
    (x-6)(x+2)=0
    x=6 only, since log(-2) is not real.

    #2.
    so far, so good. Recall that adding/subtracting logs means multiplying/dividing numbers. So, you have

    ln sqrt(x)-ln y^3 - ln (z-2)
    ln(√x/(y^3(z-2))

    That's all you can do.

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