Question

5^{x+1}-5^{x+2}=-2500. Find x

Answer 1

x is 3

Explanation:

`{5}^((x + 1)) - {5}^((x + 2)) = - 2500 \\`

divide all sides by -1:

`{5}^((x + 2)) - 5 {}^((x + 1)) = 2500`

from law of indices:

`( {5}^(x) . {5}^(2) ) - ( {5}^(x) . {5}^(1) ) = 2500`

factorise out 5^x:

`{5}^(x) ( {5}^(2) - {5}^(1) ) = 2500 \\ {5}^(x) (20) = 2500 \\ {5}^(x) = 125 \\ {5}^(x) = {5}^(3) \\ x = 3`