Question

Plz help me solve this pre calc problem, I have to condense using the properties of log

Answer 1

Given:

$\log \left(x^{2}\right)+\log \sqrt{x^{3}+1}$

To find:

The condense of the logarithmic function.

Solution:

$\log \left(x^{2}\right)+\log \sqrt{x^{3}+1}$

Apply log rule:

$\log _{c}(a)+\log _{c}(b)=\log _{c}(a b)$

Using the log rule:

$\log _{10}\left(x^{2}\right)+\log _{10}(\sqrt{x^{3}+1})=\log _{10}\left(x^{2} \sqrt{x^{3}+1}\right)$

$\log \left(x^{2}\right)+\log \sqrt{x^{3}+1}=\log \left(x^{2} \sqrt{x^{3}+1}\right)$