If-3-log-3-7-x-7-log-7-3-x-then-the-value-of-x-will-be-

Question Number 138091 by liberty last updated on 10/Apr/21

I f 3^{{(\log_{3} 7)}^{x}} = 7^{{(\log_{7} 3)}^{x}}, t h e n t h e

v a l u e o f x w i l l b e \dots

Answered by mitica last updated on 10/Apr/21

{({l o g}_{3} 7)}^{x} = a \Rightarrow {({l o g}_{7} 3)}^{x} = \frac{1}{a}

3^{a} = 7^{\frac{1}{a}} \Rightarrow a = {l o g}_{3} 7^{\frac{1}{a}} \Rightarrow a = {({l o g}_{3} 7)}^{\frac{1}{2}} \Rightarrow x = \frac{1}{2}

Answered by Ankushkumarparcha last updated on 10/Apr/21

S o l u t i o n : T a k i n g^{'} \log_{e}^{'} o n b o t h s i d e s .

{(\log_{3} 7)}^{x} \log_{e} (3) = {(\log_{7} 3)}^{x} \log_{e} (7)

{(\frac{\log_{3} 7}{\log_{7} 3})}^{x} = \frac{\log_{e} 7}{\log_{e} 3},

{(\frac{\log_{e} 7}{\log_{e} 3})}^{2 x} = \frac{\log_{e} 7}{\log_{e} 3} (∵ \log_{a} b = \frac{\log_{e} b}{\log_{e} a})

B y c o m p a r i n g . W e g e t,

x = 1 / 2