Simplify some of these Natural Log Functions - help

Was absent for a few days - got make-up work, clueless - can someone please simplify these functions? Would appreciate it.
(1) Ln 5 + ln x = 1
(2) Ln 5 - ln x = 3
(3) ln 1- + ln x^2 = 10
(4) ln (x + 7) + ln (x+3) = ln 77
Might be asking a lot but any help simplifying these would be cool..

Use those formulas to evaluate each expression.

ln(a) + ln(b) = ln(ab)
ln(a) - ln(b) = ln(a/b)

1. ln(5x) = 1 [You are adding logs, so you are multiplying terms]

Then, set both sides by e:

e^(ln(5x)) = e
5x = e

Therefore, x = e/5

The process is similar for the rest of the problems.

2. ln(5/x) = 3
e^(ln(5/x)) = e³
5/x = e³
x/5 = 1/e³
x = 5/e³

3. Assume that the equation is ln(1) - ln(x²) = 10.

ln(1/x²) = 10

Then,

1/x² = e^(10)
x² = 1/e^(10)
x = ±√(1/e^(10))
x = ±(1/e^(5))

Negative value is accepted since x is squared, yielding positive value.

4. ln((x + 7)(x + 3)) = ln(77)

Then,

(x + 7)(x + 3) = 77
x² + 10x + 21 = 77

Convert into standard form:

x² + 10x + 21 - 77 = 0
x² + 10x - 56 = 0
(x + 14)(x - 4) = 0
x = {4,-14}

However, x = -14 yields imaginary solution for both logs. Therefore, x = 4.

I hope this helps!

Ln addition works like this:
ln(a) + ln(b) = ln(a*b)
ln(a) - ln(b) = ln(a/b)
Using this info, ill show you number 1 and 2 and then you can try out the others:
1) Ln 5 + ln x = 1
ln(5*x) = 1
5*x = e^(1)
x = e/5

2) Ln 5 - ln x = 3
ln(5/x) = 3
5/x = e^3
x = 5 / (e^3)