Menu Close

given-that-log2-0-3010-log3-0-477-log5-0-699-find-the-values-of-log-0-2-




Question Number 52030 by Water last updated on 02/Jan/19
given that log2=0.3010 log3=0.477 log5=0.699  find the values of log(√((0.2)))
$${given}\:{that}\:{log}\mathrm{2}=\mathrm{0}.\mathrm{3010}\:{log}\mathrm{3}=\mathrm{0}.\mathrm{477}\:{log}\mathrm{5}=\mathrm{0}.\mathrm{699} \\ $$$${find}\:{the}\:{values}\:{of}\:{log}\sqrt{\left(\mathrm{0}.\mathrm{2}\right)} \\ $$$$ \\ $$
Answered by afachri last updated on 02/Jan/19
log ((2/(10)))^(0.5) = 0.5 log ((2/(10)))                            = 0.5 (log 2 − log 10)                            = 0.5 (0.3010 − 1)                             = − 0.3495
$$\mathrm{log}\:\left(\frac{\mathrm{2}}{\mathrm{10}}\right)^{\mathrm{0}.\mathrm{5}} =\:\mathrm{0}.\mathrm{5}\:\mathrm{log}\:\left(\frac{\mathrm{2}}{\mathrm{10}}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\mathrm{0}.\mathrm{5}\:\left(\mathrm{log}\:\mathrm{2}\:−\:\mathrm{log}\:\mathrm{10}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\mathrm{0}.\mathrm{5}\:\left(\mathrm{0}.\mathrm{3010}\:−\:\mathrm{1}\right)\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:−\:\mathrm{0}.\mathrm{3495} \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *