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Math Help - Exponential Equation

  1. #1
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    Exponential Equation

    I was given 3^x-1= 1/9
    I took the log of both and got log3*x-1=log(1/9)
    At this point I know I have to divide log(1/9)by log(3) to isolate the x but I do not know how to do this without a calculator. Is there a way to do this problem without a calculator?
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by kpatch60 View Post
    I was given 3^x-1= 1/9
    I took the log of both and got log3*x-1=log(1/9)
    At this point I know I have to divide log(1/9)by log(3) to isolate the x but I do not know how to do this without a calculator. Is there a way to do this problem without a calculator?
    Spoiler:
    Hint: \log(1/9) = -2\log 3
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  3. #3
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    So just rewrite as 3^-2 and move the exponent to the front position? Thanks, I never looked at it like that.
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  4. #4
    A Plied Mathematician
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    Do you mean

    3^{x-1}=\frac{1}{9}, or

    3^{x}-1=\frac{1}{9}?
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