5^x*2^x=0.01

Solution for 5^x*2^x=0.01 equation:

5^x*2^x=0.01

We move all terms to the left:

5^x*2^x-(0.01)=0

We add all the numbers together, and all the variables

5^x*2^x-0.01=0

Wy multiply elements

10x^2-0.01=0

a = 10; b = 0; c = -0.01;
Δ = b2-4ac
Δ = 02-4·10·(-0.01)
Δ = 0.4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-\sqrt{0.4}}{2*10}=\frac{0-\sqrt{0.4}}{20}
=-\frac{\sqrt{}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+\sqrt{0.4}}{2*10}=\frac{0+\sqrt{0.4}}{20}
=\frac{\sqrt{}}{20}
$