Solve the equation 1000 * 1.1 x = 100 * 1.1 X

Solve the equation 1000 * 1.1 x = 100 * 1.1 X

A:
X power of 1000 * 1.1 = x power of 100 * 1.1
(1000-100)*1.1^x=0
900*1.1^x=0
1.1^x=0
The equation has no real solution
X of (1000 * 1.1) = (100 * 1.1)
(1000^x)*(1.1^x)=(100^x)*(1.1^x)
Because: 1.1 ^ x > 0
So:
1000^x=100^x
10^(3x)=10^(2x)
3x=2x
The solution is: x = 0