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Precalc

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1. 1/3log base 8 of (x+1)=2log base 8 of 3-(2/3)log base 8 of (x+1)

2. 2^x+8 times 2^=x all over 2 = 3

3. if log base a of 3= x and log base a of 2 = y, find each of thefollowing in terms of x and y

log base a (18a^3)

thanks!!

  • Precalc -

    1.
    omitting all the base 8 stuff, we have

    1/3 log(x+1) = 2log3 - 2/3 log(x+1)
    log(x+1) = 2log3
    log(x+1) = log9
    x+1=9
    x=8

    2.
    not sure what the extra = means.

    (2^x + 8*2^x)/2 = 3
    9*2^x/2 = 3
    9*2^x = 6
    2^x = 3/2
    x = ln(3/2)/ln2
    May be a typo here; it's an odd answer

    3.
    omitting all the base a stuff,
    log(18x^3) = log18 + loga^3
    = log9+log2+3loga
    = 2log3 + log2 + 3loga
    = 2x+y+3

  • Precalc -

    oops it was 2^-x



    im confused why would you omit the bases?

  • Precalc -

    just for readability. Got tired of typing it in. And, until you need to resolve the base, it doesn't really matter. In #1, the equations work regardless of base, since we are working with logs on both sides of the equation.

    In #3, the base didn't matter until we could use it to say that log_a(a) = 1

    For #2, I suspected it might have been 2^-x, and it helps a lot!

    (2^x + 8*2^-x)/2 = 3
    2^x + 8/2^x = 6
    if you let u = 2^x, then you have
    u+8/u = 6
    u^2 + 8 = 6u
    u^2 - 6u + 8 = 0
    (u-4)(u-2) = 0
    u=4 or u=2
    2^x=4 or 2^x=2
    x=2 or x=1

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