# Thread: Sum and/or Difference of Logs

1. ## Sum and/or Difference of Logs

Write each sum as a sum and/or difference of logs. Express powers as factors.

Before getting to the questions, what does the question mean by "Express powers as factors"?

QUESTIONS:

(1) log_2[(a/b^2)], where a > 0, b > 0

(2) ln[x(sqrt{1 + x^2)], where x > 0

2. "express powers as factors" tells you to use the power rule for logs, i.e.
$\log_b{x^n} = n\log_b{x}$
note that the power "n" is now a factor.

use the quotient property of logs to break it apart ...

$\log_2 \left(\frac{a}{b^2}\right) =\log_2{a} - \log_2{b^2}$

now finish this one (express powers as factors) and then try the second one yourself ... you'll be using the product property of logs.

3. ## Great....

This is exactly what I was looking for.

Thanks!