Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers.
-$\log _ { b } \left( \frac { m ^ { 7 } p ^ { 5 } } { n ^ { 3 } b ^ { 2 } } \right)$
A) $\log _ { b } m ^ { 7 } + \log _ { b } p ^ { 5 } + \log _ { b } n ^ { 3 } - \log _ { b } b ^ { 2 }$
B) $7 \log _ { b } m + 5 \log _ { b } p - 3 \log _ { b } n + 2$
C) $7 \log _ { b } m + 5 \log _ { b } p - 3 \log _ { b } n - 2$
D) $m ^ { 7 } p ^ { 5 } - n ^ { 3 } b ^ { 2 }$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, the expression can be rewritten as the sum of the logarithms of the numerator's factors minus the sum of the logarithms of the denominator's factors. The coefficient of each logarithm corresponds to the exponent of its base inside the logarithm. The logarithm of $b^2$ simplifies to 2 because $\log_b(b^2) = 2$.

Use the Properties of Logarithms to Rewrite the Expression log⁡b(m7p5n3b2)\log _ { b } \left( \frac { m ^ { 7 } p ^ { 5 } } { n ^ { 3 } b ^ { 2 } } \right)logb​(n3b2m7p5​)

Use the Properties of Logarithms to Rewrite the Expression $\log _ { b } \left( \frac { m ^ { 7 } p ^ { 5 } } { n ^ { 3 } b ^ { 2 } } \right)$