20. Exponential and Logarithmic Functions

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

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

Use the power property to rewrite the log expression.

${\log }_2{(x+1)}^2$

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.

${\log }_{5}24-{\log }_{5}8$

Use the power property to rewrite the log expression.

${\log }_6\frac{1}{\sqrt{m}}$

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

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

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

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

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.

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

Rewrite the log expression as the sum or difference of multiple logs.

${\log }_{10}\left(\frac{8x^3}{5y}\right)$

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

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

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

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

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 single log.

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

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

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