13. Inverse, Exponential, & Logarithmic Functions

Rewrite the sum as a single logarithm. Further simplify if possible.

${\log }_{10}x+{\log }_{10}(x+2)$

Rewrite the log expression as a single log.

$3{\log }_{4}a-\frac{1}{2}{\log }_4(b+1)+{\log }_4\left(4c\right)$

Rewrite the difference as a single logarithm. Further simplify if possible.

${\log }_{10}\left(8x^2\right)-{\log }_{10}\left(2x\right)$

Rewrite the log expression as a difference of multiple logs. Further simplify if possible.

${\log }_2\left(\frac{x}{6}\right)$

Rewrite the sum as a single logarithm. Further simplify if possible.

${\log }_5\frac{1}{3}+{\log }_{5}12y$