Answer:
x is 3
Step-by-step explanation:
[tex] {5}^{(x + 1)} - {5}^{(x + 2)} = - 2500 \\ [/tex]
divide all sides by -1:
[tex] {5}^{(x + 2)} - 5 {}^{(x + 1)} = 2500[/tex]
from law of indices:
[tex]( {5}^{x} . {5}^{2} ) - ( {5}^{x} . {5}^{1} ) = 2500[/tex]
factorise out 5^x:
[tex] {5}^{x} ( {5}^{2} - {5}^{1} ) = 2500 \\ {5}^{x} (20) = 2500 \\ {5}^{x} = 125 \\ {5}^{x} = {5}^{3} \\ x = 3[/tex]
