Question

Evaluate the logarithmic expression.log464

Answer 1

Answer:

3

Explanation:

Given the logarithmic expression:

$\log_464$

First, express 64 as a power of 4:

$\log_44^3$

Next, apply the power law of logarithms:

$\begin{gathered} \log a^n=n\log a \\ \implies\log_44^3=3\log_44 \end{gathered}$

Finally, by the unity law:

$\begin{gathered} \log_aa=1 \\ \implies3\;\log_44=3\times1=3 \end{gathered}$

The result of the evaluation is 3.