3-5-x-5-3-x-solve-for-x-

Question Number 175685 by Linton last updated on 05/Sep/22

3^{5^{x}} = 5^{3^{x}}

s o l v e f o r x

Answered by mahdipoor last updated on 05/Sep/22

l n (l n (3^{5^{x}})) = l n (l n (5^{3^{x}})) \Rightarrow

l n (5^{x} \times l n (3)) = l n (3^{x} \times l n (5)) \Rightarrow

x . l n 5 + l n (l n 3) = x . l n 3 + l n (l n 5) \Rightarrow

x = \frac{l n (l n 5) - l n (l n 3)}{l n 5 - l n 3} = \frac{l n (\frac{l n 5}{l n 3})}{l n (\frac{5}{3})} =

{l o g}_{\frac{5}{3}} ({l o g}_{3} 5)

Answered by Rasheed.Sindhi last updated on 06/Sep/22

3^{5^{x}} = 5^{3^{x}}

5^{x} \log 3 = 3^{x} \log 5

{(\frac{5}{3})}^{x} = \frac{\log 5}{\log 3} = \log_{3} 5

x (\log 5 - \log 3) = \log (\log_{3} 5)

x = \frac{\log (\log_{3} 5)}{\log 5 - \log 3}

Commented by Rasheed.Sindhi last updated on 05/Sep/22

T h a n k y o u f o r c o r r e c t i o n s i r!