Precalc

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How to solve for x:

2^(2x) + 2^(x) -12 = 0

Steps too

I tried solving this but I ended with ln(12) / 2ln(2) + ln(2) but the real answer is supposed to be ln(3) / ln(2) or 1.585

  • Precalc -

    let 2^x= y
    then your equation becomes
    y^2 + y - 12 = 0
    (y+4)(y-3) = 0
    so y = -4 or y = 3
    then
    2^x= -4, which is not possible
    or
    2^x = 3
    ln both sides
    ln(2x) = ln3
    x ln2 = ln 3
    x = ln3/ln2 = appr. 1.58

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