Expand into a sum and/or difference of logarithms. Assume all variables represent positive real numbers. $\log _ { 7 } x ^ { y }$
A) $\log _ { 7 y } x$
B) $\log _ { 7 } x ^ { \log _ { 7 } y }$
C) $\left( \log _ { 7 } x \right) ^ { y }$
D) $y \log _ { 7 } x$

Question

Quizplus · Accepted Answer

The logarithm of a power, such as $\log_b(x^y)$, can be expanded into the product of the exponent and the logarithm of the base, which is $y \log_b(x)$. Therefore, $\log_7(x^y)$ expands to $y \log_7(x)$.

Expand into a Sum And/or Difference of Logarithms log⁡7xy\log _ { 7 } x ^ { y }log7​xy

Expand into a Sum And/or Difference of Logarithms $\log _ { 7 } x ^ { y }$