Help solving logarithms

I really need help solving these problems in my calculus summer packet.

1) log10^12

2) ln e^19

3) e^ 2 ln 5

4) write log (2x^2 y^3) as a sum of logarithms,

5) write ln x^3 - 4ln(xy) as a single logarithm.

6) 2^ 3x-2 = 5

7) log(x+3) + log x = 1

8) (ln x)^ 2 = ln x^ 2

HELP / EXPLANATIONS to any of those problems would be greatly appreciated !
thankyou :)

1.
log 10^12 = 12 log 10 = 12(1) = 12

2.
ln e^19 = 19 ln e = 19(1) = 19

3.
e^(2 ln 5) = e^(ln (5^2)) = e^(ln 25)

4.
log (2x^2 y^3) = log 2 + x^2 + log y^3 = log 2 + 2 log x + 3 log y

5.
ln x^3 - 4 ln (xy) = ln x^3 - ln (xy)^4 = ln (x^3 / (xy)^4) = ln (x^3 / (x^4 y^4)) = ln (1 / (xy^4))

7.
log (x+3) + log x = 1
log (x+3)(x) = 1
x^3 + 3x = 10^1
x^3 + 3x - 10 = 0
(x + 5)(x - 2) = 0
x = -5 or x = 2

8.
(ln x)^2 = ln (x^2)
(ln x)^2 = 2 ln x
(ln x)^2 / ln x = 2
ln x = 2
x = e^2