Express the given logarithm as a sum and/or difference of logarithms. Simplify, if possible. Assume that all variables represent positive real numbers.
-$\log _{n} \sqrt[3]{\frac{2 x^{6}}{z^{9}}}$
A) $\frac{1}{3} \log _{n} 2-2 \log _{n} x-3 \log _{n} z$
B) $\frac{1}{3} \log _{n} 2+6 \log _{n} x-9 \log _{n} z$
C) $\frac{1}{3} \log _{n} 2+2 \log _{n} x-3 \log _{n} z$
D) $\frac{1}{3} \log _{n} 2+2 \log _{n} x+3 \log _{n} z$

Question

Quizplus · Accepted Answer

The given logarithm can be expressed as a sum and/or difference of logarithms by applying the properties of logarithms: $\log _{n} \sqrt[3]{\frac{2 x^{6}}{z^{9}}} = \frac{1}{3} \log _{n} 2 + \frac{1}{3} \log _{n} x^{6} - \frac{1}{3} \log _{n} z^{9} = \frac{1}{3} \log _{n} 2 + 2 \log _{n} x - 3 \log _{n} z$.

Express the Given Logarithm as a Sum And/or Difference of Logarithms