Question

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

Answer 1

Answer:

x is 3

Step-by-step 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:

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