Please check the following logarithms and let me know if they are correct. If they are not, please point out the mistake I am making and what to fix You will be thanked!

1. log4(x^2) - log4(4x - 4) = 0

log4(x^2/4x-4) = 0

log4(x^2/4(x)+4(-1)) = 0

log4(x^2/4(x-1)) = 0

4log4(x^2/4(x-1) = 4^0

4log4(x^2/4(x-1) = 1

x^2/4(x-1) = 1

x^2/1 = 4(x-1)

x^2 = 4(x-1)

x^2 = (4(x) + 4(-1))

x^2 = (4x -4)

x^2 = 4x - 4

x^2 - 4x = -4

x^2 - 4x + 4 = 0

(x - 2)(x - 2) = 0

(x-2)^2 = 0

x- 2 = 0

x = 2

2. log2(x) + log2(x + 2) = 3

log2((x)(x + 2)) = 3

log2(x(x + 2)) = 3

2log2(x(x + 2)) = 2^3

2log2(x(x + 2)) = 8

x(x+2) = 8

(x(x) + x(2)) = 8

(x^2 + 2x) = 8

x^2 + 2x = 8

x^2 + 2x - 8 = 0

(x + 4)(x - 2) = 0

x + 4 = 0

x - 2 = 0

x = -4

x = 2

x = -4, 2

3. 2^(2x + 2) = 64

2^(2x + 2) = 2^6

(2x + 2) = 6

2x + 2 = 6

2x = -2x + 6

2x = 4

2x/2 = 4/2

x = 4/2

x = 2

4. 3^(x^2 + 2x) = 27

3^(x^2 + 2x) = 3^3

(x^2 + 2x) = 3

x^2 + 2x = 3

x^2 + 2x - 3 = 0

(x + 3)(x-1) = 0

x + 3 = 0

x - 1 = 0

x = -3

x = 1

x = -3, 1

5. 4^x = 63

ln(4^x) = ln(63)

xln(4) = ln(63)

xln(4)/ln(4) = ln(63)/ln(4)

x = ln(63)/ln(4)

6. 10^4x = 101

ln(10^4x) = ln(101)

4xln(10) = ln(101)

4xln(10)/4ln(10) = ln(101)/4ln(10)

x = ln(101)/4ln(10)[/LEFT]