Question

Evaluate the logarithmic expression.log464

Answer 1

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*1=3 \end{gathered}`

The result of the evaluation is 3.