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why-log0-9-2log3-1-




Question Number 6878 by sarathon last updated on 01/Aug/16
why log0.9=2log3−1 ??
$${why}\:{log}\mathrm{0}.\mathrm{9}=\mathrm{2}{log}\mathrm{3}−\mathrm{1}\:?? \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$
Answered by Tawakalitu. last updated on 01/Aug/16
Log 0.9  = log((9/(10)))  = log9 − log10  = log3^2  − log10  = 2log3 − 1    since, log_(10) ^(10)  = 1
$${Log}\:\mathrm{0}.\mathrm{9} \\ $$$$=\:{log}\left(\frac{\mathrm{9}}{\mathrm{10}}\right) \\ $$$$=\:{log}\mathrm{9}\:−\:{log}\mathrm{10} \\ $$$$=\:{log}\mathrm{3}^{\mathrm{2}} \:−\:{log}\mathrm{10} \\ $$$$=\:\mathrm{2}{log}\mathrm{3}\:−\:\mathrm{1} \\ $$$$ \\ $$$${since},\:{log}_{\mathrm{10}} ^{\mathrm{10}} \:=\:\mathrm{1} \\ $$

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