ln(x-5)-ln(x+2)=ln(x-10)-ln(x+10)

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Solution for ln(x-5)-ln(x+2)=ln(x-10)-ln(x+10) equation: 


Simplifying
ln(x + -5) + -1ln(x + 2) = ln(x + -10) + -1ln(x + 10)

Reorder the terms:
ln(-5 + x) + -1ln(x + 2) = ln(x + -10) + -1ln(x + 10)
(-5 * ln + x * ln) + -1ln(x + 2) = ln(x + -10) + -1ln(x + 10)
(-5ln + lnx) + -1ln(x + 2) = ln(x + -10) + -1ln(x + 10)

Reorder the terms:
-5ln + lnx + -1ln(2 + x) = ln(x + -10) + -1ln(x + 10)
-5ln + lnx + (2 * -1ln + x * -1ln) = ln(x + -10) + -1ln(x + 10)
-5ln + lnx + (-2ln + -1lnx) = ln(x + -10) + -1ln(x + 10)

Reorder the terms:
-5ln + -2ln + lnx + -1lnx = ln(x + -10) + -1ln(x + 10)

Combine like terms: -5ln + -2ln = -7ln
-7ln + lnx + -1lnx = ln(x + -10) + -1ln(x + 10)

Combine like terms: lnx + -1lnx = 0
-7ln + 0 = ln(x + -10) + -1ln(x + 10)
-7ln = ln(x + -10) + -1ln(x + 10)

Reorder the terms:
-7ln = ln(-10 + x) + -1ln(x + 10)
-7ln = (-10 * ln + x * ln) + -1ln(x + 10)
-7ln = (-10ln + lnx) + -1ln(x + 10)

Reorder the terms:
-7ln = -10ln + lnx + -1ln(10 + x)
-7ln = -10ln + lnx + (10 * -1ln + x * -1ln)
-7ln = -10ln + lnx + (-10ln + -1lnx)

Reorder the terms:
-7ln = -10ln + -10ln + lnx + -1lnx

Combine like terms: -10ln + -10ln = -20ln
-7ln = -20ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-7ln = -20ln + 0
-7ln = -20ln

Solving
-7ln = -20ln

Solving for variable 'l'.

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

Add '20ln' to each side of the equation.
-7ln + 20ln = -20ln + 20ln

Combine like terms: -7ln + 20ln = 13ln
13ln = -20ln + 20ln

Combine like terms: -20ln + 20ln = 0
13ln = 0

Divide each side by '13'.
ln = 0

Simplifying
ln = 0

The solution to this equation could not be determined.

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