Question Number 197251 by sciencestudentW last updated on 11/Sep/23
$$\mathrm{log}\:\mathrm{2}=\mathrm{0}.\mathrm{30103} \\ $$$$\mathrm{log}\:\mathrm{125}=? \\ $$
Answered by mr W last updated on 26/Sep/23
$$\mathrm{log}\:\mathrm{2}={a} \\ $$$$\mathrm{log}\:\mathrm{125}=\mathrm{log}\:\mathrm{5}^{\mathrm{3}} =\mathrm{3}\:\mathrm{log}\:\mathrm{5}=\mathrm{3}\left(\:\mathrm{log}\:\mathrm{10}−\mathrm{log}\:\mathrm{2}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{3}\left(\mathrm{1}−{a}\right)=\mathrm{3}\left(\mathrm{1}−\mathrm{0}.\mathrm{30103}\right)=\mathrm{2}.\mathrm{09691} \\ $$