Question

Find the value of log 3√7to base 7

Answer 1

$heya \\ \\ \\ we \: know \: that \\ \\ \\ log(mn) = log(m) + log(n) \\ \\ and \\ \\ \\ log_{x {}^{} }(x {}^{n} ) = n \times log_{x}(x) = n \times 1 = n \\ \\ \\ \\ \\ = > \\ \\ log_{7}(3 \sqrt{7} ) = log_{7}(3) + log_{7}( \sqrt{7} ) \\ \\ \\ \\ = > \\ \\ log_{7}(3) + 1 \div 2 \\ \\ \\ = > \\ \\ \\ log_{10}(3) \div ( log_{10}(7) ) \: \: \: \: + 1 \div 2$