Question Number 117140 by aurpeyz last updated on 09/Oct/20
Answered by bemath last updated on 10/Oct/20
![=2[ 1−log _7 (3)−log _7 (5)]+ 7 [2 log _7 (5)−log _7 (3)−2log _7 (2)]− 2 [1−log _7 (3) ] = 2[ 1−2log _7 (3)−2log _7 (5) + 14 log _7 (5)−7log _7 (3)−14log _7 (2) − 2 +2log _7 (3) = 4−9log _7 (3)+10log _7 (5)−14log _7 (2) =4−9.(0.566)+10.(0.827)−14.(0.356)](https://www.tinkutara.com/question/Q117155.png)
$$=\mathrm{2}\left[\:\mathrm{1}−\mathrm{log}\:_{\mathrm{7}} \left(\mathrm{3}\right)−\mathrm{log}\:_{\mathrm{7}} \left(\mathrm{5}\right)\right]+\: \\ $$$$\mathrm{7}\:\left[\mathrm{2}\:\mathrm{log}\:_{\mathrm{7}} \left(\mathrm{5}\right)−\mathrm{log}\:_{\mathrm{7}} \left(\mathrm{3}\right)−\mathrm{2log}\:_{\mathrm{7}} \left(\mathrm{2}\right)\right]− \\ $$$$\mathrm{2}\:\left[\mathrm{1}−\mathrm{log}\:_{\mathrm{7}} \left(\mathrm{3}\right)\:\right]\: \\ $$$$=\:\mathrm{2}\left[\:\mathrm{1}−\mathrm{2log}\:_{\mathrm{7}} \left(\mathrm{3}\right)−\mathrm{2log}\:_{\mathrm{7}} \left(\mathrm{5}\right)\:+\right. \\ $$$$\mathrm{14}\:\mathrm{log}\:_{\mathrm{7}} \left(\mathrm{5}\right)−\mathrm{7log}\:_{\mathrm{7}} \left(\mathrm{3}\right)−\mathrm{14log}\:_{\mathrm{7}} \left(\mathrm{2}\right)\:− \\ $$$$\mathrm{2}\:+\mathrm{2log}\:_{\mathrm{7}} \left(\mathrm{3}\right) \\ $$$$=\:\mathrm{4}−\mathrm{9log}\:_{\mathrm{7}} \left(\mathrm{3}\right)+\mathrm{10log}\:_{\mathrm{7}} \left(\mathrm{5}\right)−\mathrm{14log}\:_{\mathrm{7}} \left(\mathrm{2}\right) \\ $$$$=\mathrm{4}−\mathrm{9}.\left(\mathrm{0}.\mathrm{566}\right)+\mathrm{10}.\left(\mathrm{0}.\mathrm{827}\right)−\mathrm{14}.\left(\mathrm{0}.\mathrm{356}\right) \\ $$