Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers.
-$\log b \sqrt [ 3 ] { \frac { x ^ { 6 } } { y ^ { 2 } z ^ { 8 } } }$
A) $2 \log _ { b } x \div \left( \frac { 2 } { 3 } \log _ { b y } \cdot \frac { 8 } { 3 } \log _ { b } z \right)$
B) $\frac { 1 } { 3 } \log _ { b } x ^ { 6 } - \log _ { b } y ^ { 2 } - \log _ { b } z ^ { 8 }$
C) $6 \log _ { b } x - 2 \log _ { b } y - 8 \log _ { b } z$
D) $2 \log _ { b } x - \frac { 2 } { 3 } \log _ { b } y - \frac { 8 } { 3 } \log _ { b } z$

Question

Quizplus · Accepted Answer

The expression can be simplified using the properties of logarithms: $\log_b \sqrt[3]{\frac{x^6}{y^2z^8}}$ can be rewritten as $\frac{1}{3}\log_b \frac{x^6}{y^2z^8}$, which simplifies further to $\frac{1}{3}(6\log_b x - 2\log_b y - 8\log_b z)$, resulting in $2\log_b x - \frac{2}{3}\log_b y - \frac{8}{3}\log_b z$.

Use the Properties of Logarithms to Rewrite the Expression log⁡bx6y2z83\log b \sqrt [ 3 ] { \frac { x ^ { 6 } } { y ^ { 2 } z ^ { 8 } } }logb3y2z8x6​​

Use the Properties of Logarithms to Rewrite the Expression $\log b \sqrt [ 3 ] { \frac { x ^ { 6 } } { y ^ { 2 } z ^ { 8 } } }$