Question

If logx=0.25
, what is logx4
? Rewrite using the power rule, then evaluate.

Answer 1

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:

\[
\boxed{0.5}
\]