Question

〖25〗^(x+1)=√(5^x )
Como achar o valor de X e fazer a prova real?

Answer 1

$25^{x+1}= \sqrt{5^x}\\\\ (5^2)^{x+1}= 5^{ \tfrac{x}{2}}\\\\\not5^{2x+2}=\not5^{ \tfrac{x}{2}}\\\\2x+2= \dfrac{x}{2}\\\\ 2\cdot(2x+2)=x\\ 4x+4=x\\ x-4x=4\\ -3x=4\\\\ x=- \dfrac{4}{3}$

Agora fazemos a prova real..

$25^{ -\tfrac{4}{3}+1}= \sqrt{5^{- \tfrac{4}{3} }}\\\\ 25^{- \tfrac{1}{3} }= 5^{\left( -\tfrac{4}{3}\right)\div2}\\\\ (5^2)^{\left(- \tfrac{1}{3}\right)}=5^{- \tfrac{4}{6}}\\\\ 5^{- \tfrac{2}{3}}=5^{- \tfrac{2}{3}}$