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Question Number 9333 by j.masanja06@gmail.com last updated on 30/Nov/16

given that log 2=0.3.show that log 5=0.7

$$\mathrm{given}\:\mathrm{that}\:\mathrm{log}\:\mathrm{2}=\mathrm{0}.\mathrm{3}.\mathrm{show}\:\mathrm{that}\:\mathrm{log}\:\mathrm{5}=\mathrm{0}.\mathrm{7} \\ $$

Answered by mrW last updated on 30/Nov/16

2×5=10  log (2×5)=log 10=1  log 2+log 5=1  log 5=1−log 2=1−0.3=0.7

$$\mathrm{2}×\mathrm{5}=\mathrm{10} \\ $$$$\mathrm{log}\:\left(\mathrm{2}×\mathrm{5}\right)=\mathrm{log}\:\mathrm{10}=\mathrm{1} \\ $$$$\mathrm{log}\:\mathrm{2}+\mathrm{log}\:\mathrm{5}=\mathrm{1} \\ $$$$\mathrm{log}\:\mathrm{5}=\mathrm{1}−\mathrm{log}\:\mathrm{2}=\mathrm{1}−\mathrm{0}.\mathrm{3}=\mathrm{0}.\mathrm{7} \\ $$

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