1000=2^x*5^x

Solution for 1000=2^x*5^x equation:

1000=2^x*5^x

We move all terms to the left:

1000-(2^x*5^x)=0

We get rid of parentheses

-2^x*5^x+1000=0

Wy multiply elements

-10x^2+1000=0

a = -10; b = 0; c = +1000;
Δ = b2-4ac
Δ = 02-4·(-10)·1000
Δ = 40000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40000}=200$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200}{2*-10}=\frac{-200}{-20}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200}{2*-10}=\frac{200}{-20}
=-10
$