Question

Resolva essa equação exponencial:

(1/5) elevado na 3x divididos por 25 elevado na 2+x é igual a 5

Answer 1

$\dfrac{\left( \dfrac{1}{5}\right)^{3x} }{25^{2+x}}=5\\\\ \left(\dfrac{1}{5} \right)^{3x}=5\cdot25^{2+x}\\\\ \left( \dfrac{1}{5^1}\right)^{3x}=5\cdot(5^2)^{2+x}\\ (5^{-1})^{3x}=5^1\cdot5^4\cdot5^{2x}\\ 5^{-3x}=5^{1+4+2x}\\ 5^{-3x}=5^{2x+5}~~(elimina~as~bases~e~conserva~os~expoentes)\\\\ \not5^{-3x}=\not5^{2x+5}\\\\ -3x=2x+5\\ -3x-2x=5\\ -5x=5\\\\ x= \dfrac{~~5}{-5}\\\\ x=-1\\\\\\ \Large\boxed{\text{S}=\{-1\}}$