1. ## Logarithmic Equations

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

$\displaystyle log_8 (x^2 - 1) - log_8(x - 1) = 2$

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.
$\displaystyle log_8 (x^2 - 1) - log_8(x - 1) = 2$
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.

$\displaystyle log_8 (x^2 - 1) - log_8(x - 1) = 2$

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 $\displaystyle \displaystyle x \neq 1$ because $\displaystyle \displaystyle \log{0}$ is undefined.

\displaystyle \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.