How do you solve ln x = 2 ln (x - 6)?

1 Answer
Jul 10, 2016

lnx - 2ln(x - 6) = 0

lnx - ln(x - 6)^2 = 0

lnx - ln(x^2 - 12x + 36) = 0

ln(x/(x^2 - 12x + 36)) = 0

x/(x^2 - 12x + 36) = e^0

x = 1(x^2 - 12x + 36)

0 = x^2 - 13x + 36

0 = (x - 9)(x - 4)

x = 9 and 4

Checking the solutions in the original equation, we find that only x = 9 works. Hence, the solution set is {9}.

Hopefully this helps!