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.