Thread: Single Logarithm

Write the expression below as a single logarithm.

(1/3) log(x^3 + 1) + (1/2) log(x^2 + 1)

Originally Posted by magentarita

Write the expression below as a single logarithm.

(1/3) log(x^3 + 1) + (1/2) log(x^2 + 1)

$\displaystyle = \log (x^3 + 1)^{1/3} + \log (x^2 + 1)^{1/2}$

$\displaystyle = \, ....$

What exactly do you mean do here?

Originally Posted by magentarita

What exactly do you do here?

First I used the log rule $\displaystyle \log A^m = m \log A$ on each term to get what I posted.

Then I anticipated that you would use the log rule $\displaystyle \log A + \log B = \log (AB) \, .....$

Understood. It is always best to use words in addition to calculations to help make things easier for students. Agree?