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. 4^x = 64

ln(4^x) = ln(24)

xln(4) = ln(24)

xln(4)/ln(4) = ln(24)/ln(4)

x = ln(24)/ln(4)

2. log4(64) = 3

3. y = e^3

e^3 = y

e = 3SQRT(y)

4. log(x) + log(x) = 2

2(log(x)) + 2(-1) = 0

2(log(x)-1) = 0

(log(x)-1) = 0

log(x)-1 = 0

log(x) = 1

10log(x) = 10

x = 10

5. 2log(x) - log(x^2) + log(2/x) + log(x)

log(x^2) - log(x^2) + log(2/x) + log(x)

log(x^2/x^2) + log(2/x) + log(x)

log((x^2/x^2)(2/x))+log(x)

log(((x^2/x^2)(2/x))(x))

log(x((x^2/x^2)(2/x)))

log(x((x^2/x^2) * 2/x))

log(x((1)*2/x))

log(x(2(1)/x))

log(x(2*1/x))

log(x(2/x))

log((1 * 2))

log((2))

log(2)