Write as the sum or difference of logarithms and fully simplify, if possible. Assume the variable
represents a positive real number.
-$\log \left( \frac { \sqrt [ 3 ] { a b } } { c ^ { 5 } } \right)$
A) $\sqrt [ 3 ] { \log a + \log b } + 5 \log c$
B) $3 \log a + \log b - 5 \log c$
C) $\frac { 1 } { 3 } \log a + \frac { 1 } { 3 } \log b - 5 \log c$
D) $\frac { 1 } { 3 } \log a + \log b - 5 \log c$

Question

Quizplus · Accepted Answer

The given expression can be simplified using the properties of logarithms: $\log \left( \frac { \sqrt [ 3 ] { a b } } { c ^ { 5 } } \right)$ can be broken down into $\log (\sqrt[3]{ab}) - \log(c^5)$. The cube root can be expressed as a power of $\frac{1}{3}$, and the power rule of logarithms ($\log(a^b) = b\log(a)$) can be applied to both terms, resulting in $\frac{1}{3}\log(a) + \frac{1}{3}\log(b) - 5\log(c)$.

Write as the Sum or Difference of Logarithms and Fully log⁡(ab3c5)\log \left( \frac { \sqrt [ 3 ] { a b } } { c ^ { 5 } } \right)log(c53ab​​)

Write as the Sum or Difference of Logarithms and Fully $\log \left( \frac { \sqrt [ 3 ] { a b } } { c ^ { 5 } } \right)$