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

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


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

Multiply ln * x
lnx + ln(x + -2) = ln(x + 2) + ln(x + -3)

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

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

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

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

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

Reorder the terms:
-2ln + 2lnx = 2ln + -3ln + lnx + lnx

Combine like terms: 2ln + -3ln = -1ln
-2ln + 2lnx = -1ln + lnx + lnx

Combine like terms: lnx + lnx = 2lnx
-2ln + 2lnx = -1ln + 2lnx

Add '-2lnx' to each side of the equation.
-2ln + 2lnx + -2lnx = -1ln + 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
-2ln + 0 = -1ln + 2lnx + -2lnx
-2ln = -1ln + 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
-2ln = -1ln + 0
-2ln = -1ln

Solving
-2ln = -1ln

Solving for variable 'l'.

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

Add 'ln' to each side of the equation.
-2ln + ln = -1ln + ln

Combine like terms: -2ln + ln = -1ln
-1ln = -1ln + ln

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

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

Simplifying
ln = 0

The solution to this equation could not be determined.

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