Given:
[tex]\log \left(x^{2}\right)+\log \sqrt{x^{3}+1}[/tex]
To find:
The condense of the logarithmic function.
Solution:
[tex]\log \left(x^{2}\right)+\log \sqrt{x^{3}+1}[/tex]
Apply log rule:
[tex]\log _{c}(a)+\log _{c}(b)=\log _{c}(a b)[/tex]
Using the log rule:
[tex]\log _{10}\left(x^{2}\right)+\log _{10}(\sqrt{x^{3}+1})=\log _{10}\left(x^{2} \sqrt{x^{3}+1}\right)[/tex]
[tex]\log \left(x^{2}\right)+\log \sqrt{x^{3}+1}=\log \left(x^{2} \sqrt{x^{3}+1}\right)[/tex]
