Question

Ln 2 - ln (3x + 2) =1

Answer 1

When you add 2 logs together, you get the log of the product.
When you subtract 2 logs, you get the log of the quotient.

Like this:

     Ln(2) - Ln(3x+2) is the Ln(2/3x+2) .

So now you have          Ln(2/3x+2)  =  1

Raise 'e' to the power of
each side of the equation:        (2/3x+2)  =  e¹

Multiply each side by (3x+2):      2 = (e) (3x+2)

Divide each side by 'e':                2/e = 3x + 2

Subtract  2  from each side:      (2/e) - 2  =  3x

Divide each side by 3:                  x = [ (2/e) - 2 ] / 3

                                                         = approx.  -0.421...  (rounded)

I checked this by writing it into the original equation in place of 'x'.
That took my about 5 tries, but it finally checked OK.

Please.  DON't use my answer unless you understand
where it came from.