Please, write the logarithm as a ratio of common logarithms

Khaleesi Herbert 2021-08-21 Answered
Please, write the logarithm as a ratio of common logarithms and natural logarithms.
\(\displaystyle{{\log}_{{x}}{\left(\frac{{3}}{{10}}\right)}}\)
a) common logarithms
b) natural logarithms

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Expert Answer

d2saint0
Answered 2021-08-22 Author has 19123 answers
a)common logarithms, here we take to the base 10
\(\displaystyle{{\log}_{{b}}{a}}={\frac{{{\log{{\left({a}\right)}}}}}{{{\log{{\left({b}\right)}}}}}}\)
\(\displaystyle{{\log}_{{x}}{\left(\frac{{3}}{{10}}\right)}}={\frac{{{\log{{\left(\frac{{3}}{{10}}\right)}}}}}{{{\log{{\left({x}\right)}}}}}}\)
b)natural logarithms, here we take to the base e
\(\displaystyle{{\log}_{{b}}{a}}={\frac{{{\ln{{\left({a}\right)}}}}}{{{\ln{{\left({b}\right)}}}}}}\)
\(\displaystyle{{\log}_{{x}}{\left(\frac{{3}}{{10}}\right)}}={\frac{{{\ln{{\left(\frac{{3}}{{10}}\right)}}}}}{{{\ln{{\left({x}\right)}}}}}}\)
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