Evaluate the expression without using a calculator. $\log _ { 2 } 16 ^ { 23 }$
A) $46$
B) $92$
C) $23$
D) $16 ^ { 23 }$
E) none of these

Question

Quizplus · Accepted Answer

We use the property $\log _ { b } a ^ { c } = c \log _ { b } a$ to write $\log_2 16^{23} = 23\log_2 16$.

We can simplify $\log_2 16$ as $\log_2 2^4 = 4 \log_2 2 = 4$. Hence, $\log_2 16^{23} = 23\cdot 4 = \boxed{	extbf{(B)}\ 92}$.

Evaluate the Expression Without Using a Calculator log⁡21623\log _ { 2 } 16 ^ { 23 }log2​1623