If logx=0.25

, what is logx4
? Rewrite using the power rule, then evaluate.

1 answer

Given that \( \log x = 0.25 \), we want to find \( \log x 4 \).

Using the power rule of logarithms, we have:

\[ \log x 4 = \log x (2^2) = 2 \log x 2 \]

Now we can express \( \log x 4 \) using the properties of logarithms. First, let's rewrite \( \log x 4 \):

\[ \log x 4 = \log (x^2) \]

Applying the power rule gives us:

\[ \log x 4 = 2 \cdot \log x \]

Now substituting \( \log x = 0.25 \):

\[ \log x 4 = 2 \cdot 0.25 = 0.5 \]

Thus, the value of \( \log x 4 \) is:

\[ \boxed{0.5} \]