log100=2(logx+log5) What is x?

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.