Math - Exponentials

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How do I approach the following problem. Please don't give answer but just guidance as to how to approach these in general. I need to be able to solve without a calculator.

3^(2x+1)-16(3^x)+5=0

  • Math - Exponentials -

    Distribute

  • Math - Exponentials -

    Eventually answered my own question. No idea what distributing has to do with anything though...

    I simplified 3^(2x+1) to ((3^x)^2)*3^x then substituted a variable for 3^x and solved the corresponding quadratic. Seems to have worked

  • Math - Exponentials -

    I think you were on the right track, except
    3^(2x+1) = 3(3^x)(3^x) = 3(3^x)^2

    so let y = 3^x to change your equation to
    3y^2 - 16y + 5 = 0
    (y - 5)(3y - 1) = 0
    y = 5 or y = 1/3

    so 3^x = 5 or 3^x = 1/3

    This cannot be solved WITHOUT a calculator

    3^x = 5
    log 3^x = log 5
    x log3 = log 5
    x = log5/log3 = appr. 1.465

    but 3^x = 1/3
    3^x = 3^-1
    x = -1

    so x = -1 or x = appr. 1.465

    both answers verify in the original

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