Math Help - Logarithmic Equations

1. 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?

2. Re: Logarithmic Equations

Originally Posted by castle
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.

3. Re: Logarithmic Equations

Originally Posted by castle
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 ....

4. 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.