Question Number 6878 by sarathon last updated on 01/Aug/16
$${why}\:{log}\mathrm{0}.\mathrm{9}=\mathrm{2}{log}\mathrm{3}−\mathrm{1}\:?? \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$
Answered by Tawakalitu. last updated on 01/Aug/16
$${Log}\:\mathrm{0}.\mathrm{9} \\ $$$$=\:{log}\left(\frac{\mathrm{9}}{\mathrm{10}}\right) \\ $$$$=\:{log}\mathrm{9}\:−\:{log}\mathrm{10} \\ $$$$=\:{log}\mathrm{3}^{\mathrm{2}} \:−\:{log}\mathrm{10} \\ $$$$=\:\mathrm{2}{log}\mathrm{3}\:−\:\mathrm{1} \\ $$$$ \\ $$$${since},\:{log}_{\mathrm{10}} ^{\mathrm{10}} \:=\:\mathrm{1} \\ $$