Question

Necesito ayuda para resolver ésta ecuación exponencial

Answer 1

Hola.

Igualamos las bases utilizando prpopiedades de las potencias
Tenemos

$(6 \frac{1}{4})^{2x-1} : (2.5)^{3x+5}= (0.4)^{x+3}$

$(\frac{25}{4})^{2x-1} : ( \frac{25}{10} )^{3x+5} = (0.4)^{x+3}$

$( (\frac{5}{2})^{2})^{2x-1} : (\frac{5}{2})^{3x+5} = (\frac{2}{5}) ^{x+3}$

$( \frac{5}{2})^{2(2x-1)-(3x+5)} = (\frac{2}{5}) ^{x+3}$

$(\frac{5}{2})^{4x-2-3x-5} = (\frac{2}{5}) ^{x+3}$

$( \frac{5}{2})^{x-7} = (\frac{5}{2}) ^{-(x+3)}$

$x -7 = -(x+3)$

$x - 7 = -x - 3$

$x + x = -3 +7$

$2x=4$

$x = \frac{4}{2}$

$x = 2$

Un cordial saludo