Apply the Inverse Property of logarithmic or exponential functions to simplify the expression below. $\log _ { 8 } 64 ^ { 2 x + 5 }$
A) $4 x + 10$
B) $16 x + 40$
C) $8 ^ { 2 x + 5 }$
D) $2 \log _ { 8 } ( 2 x + 5 )$
E) $8 \log _ { 8 } ( 2 x + 5 )$

Question

Quizplus · Accepted Answer

The expression simplifies using the property of logarithms that allows the exponent to be brought in front of the log, and knowing that $64 = 8^2$, it becomes $\log_8(8^2)^{2x+5}$, which simplifies to $(2x+5)\log_8(8^2)$. Since $\log_8(8^2) = 2$, the expression further simplifies to $2(2x+5) = 4x+10$.

Apply the Inverse Property of Logarithmic or Exponential Functions to Simplify