Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { 19 } \left( \frac { \sqrt [ 3 ] { 10 } } { n ^ { 2 } m } \right)$
A) $\frac { 1 } { 3 } \log _ { 19 } 10 - 2 \log _ { 19 } n - \log _ { 19 } m$
B) $3 \log _ { 19 } 10 - 2 \log _ { 19 } \mathrm { n } - \log _ { 19 } 3$
C) $\frac { 1 } { 3 } \log _ { 19 } 10 - 2 \log _ { 19 } n - 2 \log _ { 19 } m$
D) $\log _ { 19 } 10 - \log _ { 19 } n - \log _ { 19 } m$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, we can rewrite the expression as:
$$\log_{19}\left(\frac{\sqrt[3]{10}}{n^2m}\right) = \log_{19}{\sqrt[3]{10}} - \log_{19}(n^2) - \log_{19}m = \frac{1}{3}\log_{19}10 - 2\log_{19}n - \log_{19}m$$
Therefore, the answer is choice A.

Use Properties of Logarithms to Expand the Logarithmic Expression as Much