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Math Help - Logarithmic Equations

  1. #1
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    Logarithmic Equations

    I've tried this one and feel my answer is correct but my textbook says otherwise.

    log_8 (x^2 - 1) - log_8(x - 1) = 2

    I get an answer of 63, but my book says 15. What am I doing wrong?
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  2. #2
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    Re: Logarithmic Equations

    Quote Originally Posted by castle View Post
    I've tried this one and feel my answer is correct but my textbook says otherwise.
    log_8 (x^2 - 1) - log_8(x - 1) = 2
    I get an answer of 63, but my book says 15. What am I doing wrong?
    You are correct, the book is not.
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  3. #3
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    Re: Logarithmic Equations

    Quote Originally Posted by castle View Post
    I've tried this one and feel my answer is correct but my textbook says otherwise.

    log_8 (x^2 - 1) - log_8(x - 1) = 2

    I get an answer of 63, but my book says 15. What am I doing wrong?
    Your mistake is to think that you're wrong and the book is right.

    It is simple to check each answer and see which one is correct ....
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  4. #4
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    Re: Logarithmic Equations

    First note that \displaystyle x \neq 1 because \displaystyle \log{0} is undefined.

    \displaystyle \begin{align*} \log_8{(x^2-1)} - \log_8{(x-1)} &= 2 \\ \log_8{\left(\frac{x^2 - 1}{x - 1}\right)} &= 2 \\ \frac{x^2 - 1}{x - 1} &= 8^2 \\ \frac{x^2 - 1}{x - 1} &= 64 \\ x^2 - 1 &= 64(x - 1) \\ x^2 - 1 &= 64x - 64 \\ x^2 - 64x + 63 &= 0 \\ (x - 63)(x - 1) &= 0 \\ x - 63 &= 0 \\ x &= 63 \end{align*}

    You are correct.
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