ln(x-2)-ln(x-5)=ln(x+3)

Solution for ln(x-2)-ln(x-5)=ln(x+3) equation:

Simplifying
ln(x + -2) + -1ln(x + -5) = ln(x + 3)

Reorder the terms:
ln(-2 + x) + -1ln(x + -5) = ln(x + 3)
(-2 * ln + x * ln) + -1ln(x + -5) = ln(x + 3)
(-2ln + lnx) + -1ln(x + -5) = ln(x + 3)

Reorder the terms:
-2ln + lnx + -1ln(-5 + x) = ln(x + 3)
-2ln + lnx + (-5 * -1ln + x * -1ln) = ln(x + 3)
-2ln + lnx + (5ln + -1lnx) = ln(x + 3)

Reorder the terms:
-2ln + 5ln + lnx + -1lnx = ln(x + 3)

Combine like terms: -2ln + 5ln = 3ln
3ln + lnx + -1lnx = ln(x + 3)

Combine like terms: lnx + -1lnx = 0
3ln + 0 = ln(x + 3)
3ln = ln(x + 3)

Reorder the terms:
3ln = ln(3 + x)
3ln = (3 * ln + x * ln)
3ln = (3ln + lnx)

Add '-3ln' to each side of the equation.
3ln + -3ln = 3ln + -3ln + lnx

Combine like terms: 3ln + -3ln = 0
0 = 3ln + -3ln + lnx

Combine like terms: 3ln + -3ln = 0
0 = 0 + lnx
0 = lnx

Solving
0 = lnx

Solving for variable 'l'.

Move all terms containing l to the left, all other terms to the right.

Add '-1lnx' to each side of the equation.
0 + -1lnx = lnx + -1lnx
Remove the zero:
-1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-1lnx = 0

Divide each side by '-1'.
lnx = 0

Simplifying
lnx = 0

The solution to this equation could not be determined.