# Use common logarithms or natural logarithms and a calculator to evaluate to four

Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places $$\displaystyle{{\log}_{{40.863}}}$$

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brawnyN
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