Expand. Assume that all variables represent positive real numbers.
-$\log _ { b } \left( \frac { x y ^ { 8 } } { z ^ { 7 } } \right)$

Question

Quizplus · Accepted Answer

By the properties of logarithms, we have:

$$\log_b\left(\frac{xy^8}{z^7}ight) = \log_b(x) + \log_b\left(y^8ight) - \log_b\left(z^7ight)$$

Then, using the power property of logarithms, we have:

$$\log_b(y^8) = 8\log_b(y)$$

$$\log_b(z^7) = 7\log_b(z)$$

Substituting these back into the original expression gives:

$$\log_b\left(\frac{xy^8}{z^7}ight) = \log_b(x) + 8\log_b(y) - 7\log_b(z)$$

Therefore, the correct choice is $\boxed{	ext{B}}$.

Expand Assume That All Variables Represent Positive Real Numbers log⁡b(xy8z7)\log _ { b } \left( \frac { x y ^ { 8 } } { z ^ { 7 } } \right)logb​(z7xy8​)