To evaluate \( \log_{10} 4.5 \) using the given logarithm values, you can use the properties of logarithms as follows:

First, express \( 4.5 \) as a product:

\[
\log_{10} 4.5 = \log_{10} \left(\frac{9}{2}\right)
\]

Using the property of logarithms that says \( \log(a/b) = \log a - \log b \), we get:

\[
\log_{10} 4.5 = \log_{10} 9 - \log_{10} 2
\]

Now, express \( 9 \) as \( 3^2 \):

\[
\log_{10} 9 = \log_{10} (3^2) = 2 \times \log_{10} 3
\]

Substituting the given logarithm values:

\[
\log_{10} 4.5 = 2 \times 0.4771 - 0.3010
\]

Now, perform the calculation:

\[
\log_{10} 4.5 = 0.9542 - 0.3010 = 0.6532
\]

So, the value of \( \log_{10} 4.5 \) is 0.6532.