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

jernplate8 2021-10-20 Answered
Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places \(\displaystyle{{\log}_{{40.863}}}\)

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Expert Answer

brawnyN
Answered 2021-10-21 Author has 18704 answers
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
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