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

Please, write the logarithm as a ratio of common logarithms and natural logarithms.
$$\displaystyle{{\log}_{{8}}{\left({51}\right)}}$$
a) common logarithms
b) natural logarithms

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lobeflepnoumni
$$\displaystyle{{\log}_{{8}}{\left({51}\right)}}$$
common logarithms
$$\displaystyle{{\log}_{{b}}{a}}={\frac{{{\log{{\left({a}\right)}}}}}{{{\log{{\left({b}\right)}}}}}}={\frac{{{\log{{\left({51}\right)}}}}}{{{\log{{\left({8}\right)}}}}}}$$
natural logarithms
$$\displaystyle{{\log}_{{b}}{a}}={\frac{{{\ln{{\left({a}\right)}}}}}{{{\ln{{\left({b}\right)}}}}}}={\frac{{{\ln{{\left({51}\right)}}}}}{{{\ln{{\left({8}\right)}}}}}}$$