\(\displaystyle{{\log}_{{x}}{\left(\frac{{3}}{{7}}\right)}}\)

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 : \(\displaystyle{{\log}_{{b}}{a}}=\frac{{\ln{{a}}}}{{\ln{{b}}}}\)

\(\displaystyle{{\log}_{{x}}{\left(\frac{{3}}{{7}}\right)}}=\frac{{{\ln{{\left(\frac{{3}}{{7}}\right)}}}}}{{\ln{{x}}}}\)

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 : \(\displaystyle{{\log}_{{b}}{a}}=\frac{{\ln{{a}}}}{{\ln{{b}}}}\)

\(\displaystyle{{\log}_{{x}}{\left(\frac{{3}}{{7}}\right)}}=\frac{{{\ln{{\left(\frac{{3}}{{7}}\right)}}}}}{{\ln{{x}}}}\)