solve the equation ln(x-5)-ln(3)=ln(x-3)?

Answer 1

Remember that ln(x-5)-ln(3)=ln(x-3) can be simplified to

ln 3(x-5)=ln(x-3) or ln(3x-15)=ln(x-3)

Raise everything to the power of e.

e^(ln(3x-15))=e^(ln(x-3))

Answer 2

Because log(a/b)=log(a)-log(b), the left hand side of this equation can be rewritten as Ln((x-5)/3)=Ln(x-3)
Next, just set the arguments of these logs equal and solve:
(x-5)/3=x-3 x-5=3x-9
4=2x 2=x
Therefore, your answer is x=2.
However, since x=2 is not in the domain of either of the original logs, there is no real answer for this problem.

Answer 3

ln(x-5)-ln(3)=ln(x-3)
ln((x-5)/3)=ln(x-3)
((x-5)/3)=(x-3)
x-5=3(x-3)
x-3x=5-9
-2x=-4
x=2
but notice that:
ln(2-5)=ln(-3) which is NOT defined, so in reality, there is no solution to your equation

x

Answer 4

(x-5)/3=(x-3)
x-5=3(x-3)
x-5=3x-9
-2x=-4
x=2