Question Number 9333 by j.masanja06@gmail.com last updated on 30/Nov/16
$$\mathrm{given}\:\mathrm{that}\:\mathrm{log}\:\mathrm{2}=\mathrm{0}.\mathrm{3}.\mathrm{show}\:\mathrm{that}\:\mathrm{log}\:\mathrm{5}=\mathrm{0}.\mathrm{7} \\ $$
Answered by mrW last updated on 30/Nov/16
$$\mathrm{2}×\mathrm{5}=\mathrm{10} \\ $$$$\mathrm{log}\:\left(\mathrm{2}×\mathrm{5}\right)=\mathrm{log}\:\mathrm{10}=\mathrm{1} \\ $$$$\mathrm{log}\:\mathrm{2}+\mathrm{log}\:\mathrm{5}=\mathrm{1} \\ $$$$\mathrm{log}\:\mathrm{5}=\mathrm{1}−\mathrm{log}\:\mathrm{2}=\mathrm{1}−\mathrm{0}.\mathrm{3}=\mathrm{0}.\mathrm{7} \\ $$