Question Number 121387 by Ar Brandon last updated on 07/Nov/20
![(((81)^(1/log_5 9) +3^(3/log_(√6) 3) )/(409))[((√7))^(2/log_(25) 7) −(125)^(log_(25) 6) ]](https://www.tinkutara.com/question/Q121387.png)
$$\frac{\left(\mathrm{81}\right)^{\mathrm{1}/\mathrm{log}_{\mathrm{5}} \mathrm{9}} +\mathrm{3}^{\mathrm{3}/\mathrm{log}_{\sqrt{\mathrm{6}}} \mathrm{3}} }{\mathrm{409}}\left[\left(\sqrt{\mathrm{7}}\right)^{\mathrm{2}/\mathrm{log}_{\mathrm{25}} \mathrm{7}} −\left(\mathrm{125}\right)^{\mathrm{log}_{\mathrm{25}} \mathrm{6}} \right] \\ $$
Answered by 675480065 last updated on 07/Nov/20
![(((9^(log_9 25) +3^(log_3 6(√6)) )/(409)))[7^(log_7 25) −5^(log_5 6(√6)) ] =(((25+6(√6))/(409)))(25−6(√6)) =((1/(409)))(25^2 −36(6))=((409)/(409))=1](https://www.tinkutara.com/question/Q121388.png)
$$\left(\frac{\mathrm{9}^{\mathrm{log}_{\mathrm{9}} \mathrm{25}} +\mathrm{3}^{\mathrm{log}_{\mathrm{3}} \mathrm{6}\sqrt{\mathrm{6}}} }{\mathrm{409}}\right)\left[\mathrm{7}^{\mathrm{log}_{\mathrm{7}} \mathrm{25}} −\mathrm{5}^{\mathrm{log}_{\mathrm{5}} \mathrm{6}\sqrt{\mathrm{6}}} \right] \\ $$$$=\left(\frac{\mathrm{25}+\mathrm{6}\sqrt{\mathrm{6}}}{\mathrm{409}}\right)\left(\mathrm{25}−\mathrm{6}\sqrt{\mathrm{6}}\right) \\ $$$$=\left(\frac{\mathrm{1}}{\mathrm{409}}\right)\left(\mathrm{25}^{\mathrm{2}} −\mathrm{36}\left(\mathrm{6}\right)\right)=\frac{\mathrm{409}}{\mathrm{409}}=\mathrm{1} \\ $$
Answered by liberty last updated on 07/Nov/20
![[(9)^(log _9 (5)^2 ) +3^(log _3 ((√6))^3 ) ] [ (7)^(log _7 (25)) −(6)^(log _(25) (125)) ]×(1/(409)) = [ 25+6(√6) ][25−6(√6) ]×(1/(409)) = ( 625−216)×(1/(409)) = 1 625−216 409.0](https://www.tinkutara.com/question/Q121389.png)
$$\left[\left(\mathrm{9}\right)^{\mathrm{log}\:_{\mathrm{9}} \left(\mathrm{5}\right)^{\mathrm{2}} } +\mathrm{3}^{\mathrm{log}\:_{\mathrm{3}} \left(\sqrt{\mathrm{6}}\right)^{\mathrm{3}} } \right]\:\left[\:\left(\mathrm{7}\right)^{\mathrm{log}\:_{\mathrm{7}} \left(\mathrm{25}\right)} −\left(\mathrm{6}\right)^{\mathrm{log}\:_{\mathrm{25}} \left(\mathrm{125}\right)} \:\right]×\frac{\mathrm{1}}{\mathrm{409}} \\ $$$$=\:\left[\:\mathrm{25}+\mathrm{6}\sqrt{\mathrm{6}}\:\right]\left[\mathrm{25}−\mathrm{6}\sqrt{\mathrm{6}}\:\right]×\frac{\mathrm{1}}{\mathrm{409}} \\ $$$$=\:\left(\:\mathrm{625}−\mathrm{216}\right)×\frac{\mathrm{1}}{\mathrm{409}}\:=\:\mathrm{1} \\ $$$$\mathrm{625}−\mathrm{216} \\ $$$$\mathrm{409}.\mathrm{0} \\ $$
Commented by Ar Brandon last updated on 07/Nov/20
Cool. Thanks Sir