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Question-69413




Question Number 69413 by ahmadshah last updated on 23/Sep/19
Commented by kaivan.ahmadi last updated on 23/Sep/19
(((5×(4/5))^(log_(5/4) 4) )/5^(log_(5/4) 5) )=((5^(log_(5/4) 4) ×((4/5))^(log_(5/4) 4) )/5^(log_(5/4) 5) )=((5^(log_(5/4) 4) ×((4/5))^(log_(4/5) (1/4)) )/5^(log_(5/4) 5) )=  ((5^(log_(5/4) 4) ×(1/4))/5^(log_(5/4) 5) )=(1/4)×5^(log_(5/4) 4−log_(5/4) 5) =  (1/4)×5^(log_(5/4) (4/5)) =(1/4)×5^(−1) =(1/(20))
$$\frac{\left(\mathrm{5}×\frac{\mathrm{4}}{\mathrm{5}}\right)^{{log}_{\frac{\mathrm{5}}{\mathrm{4}}} \mathrm{4}} }{\mathrm{5}^{{log}_{\frac{\mathrm{5}}{\mathrm{4}}} \mathrm{5}} }=\frac{\mathrm{5}^{{log}_{\frac{\mathrm{5}}{\mathrm{4}}} \mathrm{4}} ×\left(\frac{\mathrm{4}}{\mathrm{5}}\right)^{{log}_{\frac{\mathrm{5}}{\mathrm{4}}} \mathrm{4}} }{\mathrm{5}^{{log}_{\frac{\mathrm{5}}{\mathrm{4}}} \mathrm{5}} }=\frac{\mathrm{5}^{{log}_{\frac{\mathrm{5}}{\mathrm{4}}} \mathrm{4}} ×\left(\frac{\mathrm{4}}{\mathrm{5}}\right)^{{log}_{\frac{\mathrm{4}}{\mathrm{5}}} \frac{\mathrm{1}}{\mathrm{4}}} }{\mathrm{5}^{{log}_{\frac{\mathrm{5}}{\mathrm{4}}} \mathrm{5}} }= \\ $$$$\frac{\mathrm{5}^{{log}_{\frac{\mathrm{5}}{\mathrm{4}}} \mathrm{4}} ×\frac{\mathrm{1}}{\mathrm{4}}}{\mathrm{5}^{{log}_{\frac{\mathrm{5}}{\mathrm{4}}} \mathrm{5}} }=\frac{\mathrm{1}}{\mathrm{4}}×\mathrm{5}^{{log}_{\frac{\mathrm{5}}{\mathrm{4}}} \mathrm{4}−{log}_{\frac{\mathrm{5}}{\mathrm{4}}} \mathrm{5}} = \\ $$$$\frac{\mathrm{1}}{\mathrm{4}}×\mathrm{5}^{{log}_{\frac{\mathrm{5}}{\mathrm{4}}} \frac{\mathrm{4}}{\mathrm{5}}} =\frac{\mathrm{1}}{\mathrm{4}}×\mathrm{5}^{−\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{20}} \\ $$

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