Step 1

Use the following property.

\(\displaystyle{{\log}_{{b}}{x}}={\frac{{{\log{{x}}}}}{{{\log{{b}}}}}}\)

Here, logarithm on the right side of the equation has the base 10. These are common logarithms.

Step 2

Simplify.

\(\displaystyle{{\log}_{{40.863}}=}{\frac{{{\log{{0.863}}}}}{{{\log{{4}}}}}}\)

\(\displaystyle={\frac{{-{0.06399}}}{{{0.60206}}}}\)

=-0.1063

Use the following property.

\(\displaystyle{{\log}_{{b}}{x}}={\frac{{{\log{{x}}}}}{{{\log{{b}}}}}}\)

Here, logarithm on the right side of the equation has the base 10. These are common logarithms.

Step 2

Simplify.

\(\displaystyle{{\log}_{{40.863}}=}{\frac{{{\log{{0.863}}}}}{{{\log{{4}}}}}}\)

\(\displaystyle={\frac{{-{0.06399}}}{{{0.60206}}}}\)

=-0.1063