Question

If logx=0.25, what is logx^4? Rewrite using the power rule, then evaluate.

Answer 1

To find \( \log x^4 \) using the power rule, we can apply the logarithmic identity that states \( \log a^b = b \log a \).

Given:
\[
\log x = 0.25
\]

We can rewrite \( \log x^4 \) using the power rule:

\[
\log x^4 = 4 \log x
\]

Substituting the value of \( \log x \):

\[
\log x^4 = 4 \cdot 0.25
\]

Now, calculate \( 4 \cdot 0.25 \):

\[
4 \cdot 0.25 = 1
\]

Therefore:

\[
\log x^4 = 1
\]

So, the final answer is:

\[
\log x^4 = 1
\]