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