Question Number 52030 by Water last updated on 02/Jan/19
$${given}\:{that}\:{log}\mathrm{2}=\mathrm{0}.\mathrm{3010}\:{log}\mathrm{3}=\mathrm{0}.\mathrm{477}\:{log}\mathrm{5}=\mathrm{0}.\mathrm{699} \\ $$$${find}\:{the}\:{values}\:{of}\:{log}\sqrt{\left(\mathrm{0}.\mathrm{2}\right)} \\ $$$$ \\ $$
Answered by afachri last updated on 02/Jan/19
$$\mathrm{log}\:\left(\frac{\mathrm{2}}{\mathrm{10}}\right)^{\mathrm{0}.\mathrm{5}} =\:\mathrm{0}.\mathrm{5}\:\mathrm{log}\:\left(\frac{\mathrm{2}}{\mathrm{10}}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\mathrm{0}.\mathrm{5}\:\left(\mathrm{log}\:\mathrm{2}\:−\:\mathrm{log}\:\mathrm{10}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\mathrm{0}.\mathrm{5}\:\left(\mathrm{0}.\mathrm{3010}\:−\:\mathrm{1}\right)\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:−\:\mathrm{0}.\mathrm{3495} \\ $$