Question

Resolva essa equação exponencial 25^4x-3 = 0,2

Answer 1

Olá!

$\\ \mathsf{25^{4x - 3} = 0,2} \\\\ \mathsf{\left ( 5^2 \right )^{4x - 3} = \frac{2}{10}} \\\\ \mathsf{5^{2(4x - 3)} = \frac{1}{5}} \\\\ \mathsf{5^{8x - 6} = 5^{- 1}}$
 
 Igualando os expoentes, já que as bases são iguais, temos:

$\\ \mathsf{8x - 6 = - 1} \\ \mathsf{8x = 5} \\ \boxed{\mathsf{x = \frac{5}{8}}}$