We'll remove the brackets from the right side:

log100=2(logx+log5)

log100=2logx +2log5

First, we'll use the power property of logarithms, for the terms of the expression:

2 log 5 = log 5^2

2log x = log x^2

We'll re-write the expression:

log100 = log x^2 + log 5^2

Since the bases are matching, we'll use the product property of logarithms:

log a + log b = log a*b

We'll put a = x^2 and b = 5^2

log x^2 + log 5^2 = log x^2*5^2

We'll write the equation:

log 100 = log x^2*5^2

Since the bases are matching, we'll apply one to one property:

100 = x^2*5^2

We'll use symmetric property:

25x^2 = 100

We'll divide by 25;

x^2 = 4

x1 = -2

x2 = 2

Since the solution of the equtaion must be positive, the first solution x1 = -2, will be rejected.

The equation will have just a solution, x = 2.