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:

\[ \log x^4 = 1 \]