Exponential Equation need help....

Solve the following equation.

2^x(5^x)=1/100 (10^x-1)^4

thanks in advance....

a^c * b^c = (a * b)^c

(2^x) * (5^x) => (2 * 5)^x = 10^x

10^x = (1/100) * (10^(x - 1))^4
10^x = (10^(-2)) * 10^(4 * (x - 1))
10^x = 10^(-2 + 4 * (x - 1))
x = -2 + 4 * (x - 1)
x = -2 + 4x - 4
x - 4x = -6
-3x = -6
x = 2

We can test the answer

(2^2) * (5^2) = (1/100) * (10^(2 - 1))^4
4 * 25 = (1/100) * (10^(1))^4
100 = (1/00) * 10000
100 = 100

It checks out