Question

If m=5^x+2/5^x+5 ,n=5^x/5^2-x and m-n=0, then find the value of x.

Answer 1

Answer:

$x = - \frac{ 1}{2}$

Given :-

• m - n = 0

$= > {5}^{( - 3)} - {5}^{(2x - 2)} = 0 \\ \\ = > {5}^{( - 3)} = {5}^{(2x - 2)} \\ as \: \: the \: \: base \: \: is \: \: equal \\ by \: \: equating \: \: the \: \: powers \: - \\ \\ = > - 3 = 2x - 2 \\ \\ = > 2x = - 3 + 2 \\ \\ = > 2x = - 1 \\ \\ = > x = - \frac{1}{2}$