Rewrite the expression as the sum and/or difference of logarithms, without using exponents. Simplify if possible.
-$\log _ { 19 } \frac { \sqrt [ 6 ] { 5 } } { y ^ { 2 } x }$
A) $\frac { 1 } { 6 } \log _ { 19 } 5 - 2 \log _ { 19 } y - 2 \log _ { 19 } x$
B) $\log _ { 19 } 5 - \log _ { 19 } y - \log _ { 19 } x$
C) $6 \log _ { 19 } 5 - 2 \log _ { 19 } y - \log _ { 19 } 6$
D) $\frac { 1 } { 6 } \log _ { 19 } 5 - 2 \log _ { 19 } y - \log _ { 19 } x$

Question

Quizplus · Accepted Answer

The expression can be rewritten using the properties of logarithms: $\log \frac{a}{b} = \log a - \log b$ and $\log a^b = b \log a$. Thus, $\log _ { 19 } \frac { \sqrt [ 6 ] { 5 } } { y ^ { 2 } x }$ becomes $\frac { 1 } { 6 } \log _ { 19 } 5 - 2 \log _ { 19 } y - \log _ { 19 } x$.

Rewrite the Expression as the Sum And/or Difference of Logarithms log⁡1956y2x\log _ { 19 } \frac { \sqrt [ 6 ] { 5 } } { y ^ { 2 } x }log19​y2x65​​

Rewrite the Expression as the Sum And/or Difference of Logarithms $\log _ { 19 } \frac { \sqrt [ 6 ] { 5 } } { y ^ { 2 } x }$