Solve for x: Ln(3x+2) - lnx = 2
Given the logarithmic equation:
`ln(3x+2) - lnx = 2`
First we will use the logarithm properties to write as a single log.
==> We know that:
`lna - lnb = ln (a/b) `
`==gt ln(3x+2) - lnx = ln((3x+2)/x) = 2`
Now we will rewrite in exponent form.
`==gt (3x+2)/x = e^2 `
`==gt 3x + 2 = e^2*x `
`==gt 3x -e^2*x = -2 `
`==gt (3-e^2) x = -2 `
`==gt x = -2/(3-e^2) ~~ 0.4557`