Rewrite the sum as a single logarithm. Further simplify if possible.
${\log }_{10}x+{\log }_{10}(x+2)$

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

${\log }_{4}4x$

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

${\log }_{3}10mn$

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

${\log }_{3}4+{\log }_{3}9$

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

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

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

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

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

${\log }_{12}\left(\frac{1}{4}\right)$

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

${\log }_5\left(\frac{125}{x}\right)$

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

${\log }_3(x^2+1)-{\log }_3(4x-2)$