Question

1.Log10(x²-12x+36)=2
2.log4 log3 log2 x=0
3.log3 [log9x+1/2+9x]=2x
4.2log4(4-4)=4-log2(-2-x)

Answer 1

1. by definition of logs
x^2 - 12x + 36 = 10^2
(x-6)^2 = 100
x-6 = ±√100 = ±10
x = 6 ± 10 = 16 or -4

2. you have the product of 3 numbers = 0
so one of them is zero
but log4 and log2 are non-zero real numbers, so
log₂x must be 0
that is, x = 1

3.not clear about your typing here.

my first reaction is to see:
3^(2x) = log₉x + 1/2 + 9x
-- that would be a horrible equation to solve

4. same thing, I have doubts about your typing.
Why have (4-4) , that would be 0 and log 0 is undefined.