Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent
positive real numbers.
-$$\log _ { b } \sqrt [ 3 ] { \frac { x ^ { 2 } } { y ^ { 4 } z ^ { 7 } } }$$
A) $2 \log _ { b } x - 4 \log _ { b } y - 7 \log _ { b } z$
B) $\frac { 2 } { 3 } \log _ { b } x - \frac { 4 } { 3 } \log _ { b } y - \frac { 7 } { 3 } \log _ { b } z$
C) $\frac { 1 } { 3 } \log _ { b } x ^ { 2 } - \log _ { b } y ^ { 4 } - \log _ { b } z ^ { 7 }$
D) $\frac { 2 } { 3 } \log _ { b } x \div \left( \frac { 4 } { 3 } \log _ { b } y \cdot \frac { 7 } { 3 } \log _ { b } z \right)$

Question

Quizplus · Accepted Answer

The expression can be simplified using the properties of logarithms: the logarithm of a quotient is the difference of the logarithms, and the logarithm of a power is the exponent times the logarithm of the base. The cube root can be expressed as a power of $1/3$, leading to the correct simplification.

Use the Properties of Logarithms to Rewrite the Expression log⁡bx2y4z73\log _ { b } \sqrt [ 3 ] { \frac { x ^ { 2 } } { y ^ { 4 } z ^ { 7 } } }logb​3y4z7x2​​

Use the Properties of Logarithms to Rewrite the Expression $\log _ { b } \sqrt [ 3 ] { \frac { x ^ { 2 } } { y ^ { 4 } z ^ { 7 } } }$