evaluate-5-log-7-5-7-log-5-7-

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) \dots

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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