Rewrite the logarithm as a ratio of common logarithms and

postillan4 2021-08-19 Answered
Rewrite the logarithm as a ratio of common logarithms and natural ones. \(\displaystyle{{\log}_{{x}}{\left(\frac{{3}}{{7}}\right)}}\)

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Expert Answer

Liyana Mansell
Answered 2021-08-20 Author has 7470 answers
\(\displaystyle{{\log}_{{x}}{\left(\frac{{3}}{{7}}\right)}}\)
Common logarithm: \(\displaystyle{{\log}_{{b}}{a}}=\frac{{\log{{a}}}}{{\log{{b}}}}\)
\(\displaystyle{{\log}_{{x}}{\left(\frac{{3}}{{7}}\right)}}=\frac{{{\log{{\left(\frac{{3}}{{7}}\right)}}}}}{{\log{{x}}}}\)
Natural logarithm : \(\displaystyle{{\log}_{{b}}{a}}=\frac{{\ln{{a}}}}{{\ln{{b}}}}\)
\(\displaystyle{{\log}_{{x}}{\left(\frac{{3}}{{7}}\right)}}=\frac{{{\ln{{\left(\frac{{3}}{{7}}\right)}}}}}{{\ln{{x}}}}\)
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