evaluate 5^(√(log 7_5 )) − 7^(√(log 5


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Question Number 74753 by necxxx last updated on 30/Nov/19

$e v a l u a t e 5^{\sqrt{\log 7_{5}}} - 7^{\sqrt{\log 5_{7}}}$
Commented by mr W last updated on 30/Nov/19

$w h a t i s \log 7_{5} ? t h e s a m e a s \log_{5} 7 ?$
Commented by Kunal12588 last updated on 30/Nov/19

$d e f i n e l o g a_{b}$
Commented by turbo msup by abdo last updated on 30/Nov/19

$p e r h a p s l o g 7_{5} m e a n {l o g}_{5} (7) . . .$
Commented by necxxx last updated on 01/Dec/19

$e x a c t l y, t h a t s w h a t i m e a n t . i o n l y$ $d i d n t r e p r e s e n t i t p r o p e r l y .$
	Answered by MJS last updated on 30/Nov/19

	$we had this before, in correct syntax$ $a^{\sqrt{\log_{a} b}} = a^{\sqrt{\frac{\ln b}{\ln a}}} =$ $[\ln (a^{\sqrt{\frac{\ln b}{\ln a}}}) = \sqrt{\frac{\ln b}{\ln a}} \times \ln a = \sqrt{\ln a \times \ln b}]$ $= e^{\sqrt{\ln a \times \ln b}}$ $\Rightarrow answer is 0$
	Commented by necxxx last updated on 01/Dec/19

	$t h a n k y o u s o m u c h . I d o u n d e r s t a n d i t$ $n o w .$
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