Write as the sum and/or difference of logarithms. Express powers as factors.
-$$\log _ { 8 } \frac { \sqrt [ 7 ] { x } \sqrt [ 3 ] { y } } { z ^ { 2 } }$$
A) $\frac { 1 } { 7 } \log _ { 8 } x + \frac { 1 } { 3 } \log _ { 8 } y - 2 \log _ { 8 } z$
B) $\frac { 7 } { 8 } \log _ { 8 } x + \frac { 3 } { 8 } \log _ { 8 } y - \frac { 2 } { 8 } \log _ { 8 } z$
C) $7 \log _ { 8 } x + 3 \log _ { 8 } y - 2 \log _ { 8 } z$
D) $\frac { 1 } { 7 } \log _ { 8 } x \cdot \frac { 1 } { 3 } \log _ { 8 } y \div 2 \log _ { 8 } z$

Question

Quizplus · Accepted Answer

The properties of logarithms allow us to write the logarithm of a quotient as the difference of logarithms and the logarithm of a product as the sum of logarithms. Additionally, the logarithm of a power can be expressed as the exponent times the logarithm of the base. Thus, $\log _ { 8 } \frac { \sqrt [ 7 ] { x } \sqrt [ 3 ] { y } } { z ^ { 2 } }$ simplifies to $\frac { 1 } { 7 } \log _ { 8 } x + \frac { 1 } { 3 } \log _ { 8 } y - 2 \log _ { 8 } z$.

Write as the Sum And/or Difference of Logarithms log⁡8x7y3z2\log _ { 8 } \frac { \sqrt [ 7 ] { x } \sqrt [ 3 ] { y } } { z ^ { 2 } }log8​z27x​3y​​

Write as the Sum And/or Difference of Logarithms $\log _ { 8 } \frac { \sqrt [ 7 ] { x } \sqrt [ 3 ] { y } } { z ^ { 2 } }$