ln(x-3)-ln(x+10)=ln(x-2)-ln(x+3)

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Solution for ln(x-3)-ln(x+10)=ln(x-2)-ln(x+3) equation: 


Simplifying
ln(x + -3) + -1ln(x + 10) = ln(x + -2) + -1ln(x + 3)

Reorder the terms:
ln(-3 + x) + -1ln(x + 10) = ln(x + -2) + -1ln(x + 3)
(-3 * ln + x * ln) + -1ln(x + 10) = ln(x + -2) + -1ln(x + 3)
(-3ln + lnx) + -1ln(x + 10) = ln(x + -2) + -1ln(x + 3)

Reorder the terms:
-3ln + lnx + -1ln(10 + x) = ln(x + -2) + -1ln(x + 3)
-3ln + lnx + (10 * -1ln + x * -1ln) = ln(x + -2) + -1ln(x + 3)
-3ln + lnx + (-10ln + -1lnx) = ln(x + -2) + -1ln(x + 3)

Reorder the terms:
-3ln + -10ln + lnx + -1lnx = ln(x + -2) + -1ln(x + 3)

Combine like terms: -3ln + -10ln = -13ln
-13ln + lnx + -1lnx = ln(x + -2) + -1ln(x + 3)

Combine like terms: lnx + -1lnx = 0
-13ln + 0 = ln(x + -2) + -1ln(x + 3)
-13ln = ln(x + -2) + -1ln(x + 3)

Reorder the terms:
-13ln = ln(-2 + x) + -1ln(x + 3)
-13ln = (-2 * ln + x * ln) + -1ln(x + 3)
-13ln = (-2ln + lnx) + -1ln(x + 3)

Reorder the terms:
-13ln = -2ln + lnx + -1ln(3 + x)
-13ln = -2ln + lnx + (3 * -1ln + x * -1ln)
-13ln = -2ln + lnx + (-3ln + -1lnx)

Reorder the terms:
-13ln = -2ln + -3ln + lnx + -1lnx

Combine like terms: -2ln + -3ln = -5ln
-13ln = -5ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-13ln = -5ln + 0
-13ln = -5ln

Solving
-13ln = -5ln

Solving for variable 'l'.

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

Add '5ln' to each side of the equation.
-13ln + 5ln = -5ln + 5ln

Combine like terms: -13ln + 5ln = -8ln
-8ln = -5ln + 5ln

Combine like terms: -5ln + 5ln = 0
-8ln = 0

Divide each side by '-8'.
ln = 0

Simplifying
ln = 0

The solution to this equation could not be determined.

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