# Please, write the logarithm as a ratio of common logarithms

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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d2saint0
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
$$\displaystyle{{\log}_{{b}}{a}}={\frac{{{\ln{{\left({a}\right)}}}}}{{{\ln{{\left({b}\right)}}}}}}$$
$$\displaystyle{{\log}_{{x}}{\left(\frac{{3}}{{10}}\right)}}={\frac{{{\ln{{\left(\frac{{3}}{{10}}\right)}}}}}{{{\ln{{\left({x}\right)}}}}}}$$