Use the properties of logarithms to find the exact value of the expression. Do not use a calculator.
-$\log _ { 4 } 21 \cdot \log _ { 21 } 64$
A) 21
B) 4
C) 64
D) 3

Question

Quizplus · Accepted Answer

The expression can be simplified using the change of base formula and the property of logarithms that $\log_a b \cdot \log_b c = \log_a c$. Applying these, the expression simplifies to $\log_4 64$, which equals 3 because $4^3 = 64$.

Use the Properties of Logarithms to Find the Exact Value log⁡421⋅log⁡2164\log _ { 4 } 21 \cdot \log _ { 21 } 64log4​21⋅log21​64

Use the Properties of Logarithms to Find the Exact Value $\log _ { 4 } 21 \cdot \log _ { 21 } 64$