Natural Log Question?

2ln(x) - 3ln(x) = 4
-ln(x) = 4
Antilog
ln (x)^-1 = 4
x^-1 = e^4
x = 1/e^4 = e^-4

2 ln (x) - ln (x^3) = 4
2 ln (x) - 3 ln (x) = 4
-ln(x) = 4
ln(x) = -4
x = e^(-4) = 1/e^4 ≈ 0.01832

Combine it into one log using the rules of logs

ln(x^2) - ln(x^3) = 4
ln(x^2/x^3) = 4
ln(1/x) = 4

Now exponentiate both sides
1/x = e^4

log(a^b) = b * log(a)

2 * ln(x) - ln(x^3) = 4
2 * ln(x) - 3 * ln(x) = 4
-ln(x) = 4
ln(x) = -4
x = e^(-4)