1/5^2x=125

Solution for 1/5^2x=125 equation:

1/5^2x=125

We move all terms to the left:

1/5^2x-(125)=0


Domain of the equation: 5^2x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-125*5^2x+1=0

Wy multiply elements

-625x^2+1=0

a = -625; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-625)·1
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-50}{2*-625}=\frac{-50}{-1250}
=1/25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+50}{2*-625}=\frac{50}{-1250}
=-1/25
$