Rewrite the log expression as a sum of multiple logs. Further simplify if possible.
$lo{g}_{10}(5\cdot 7)$

Rewrite the log expression as a single log.

${\log }_{3}5+2{\log }_{3}x-{\log }_{3}2$

Rewrite the log expression as a single log.

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

Determine if the given log statement is true or false. 

${\log }_{2}48={\log }_{2}3+4{\log }_{2}2$

Determine if the given log statement is true or false. 

${\log }_3\left(\frac{324}{4\sqrt{3}}\right)=4{\log }_{3}3+{\log }_{3}3-\frac{1}{2}{\log }_{3}4$

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.

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