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

asked Jan 20, 2022 129k views

4 votes

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5 votes

Answer:

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:

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

Vitoke answered Jan 25, 2022

7.9k points

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