(x-8)-ln(x+7)=ln(x-10)-ln(x+8)

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Solution for (x-8)-ln(x+7)=ln(x-10)-ln(x+8) equation:


Simplifying
(x + -8) + -1ln(x + 7) = ln(x + -10) + -1ln(x + 8)

Reorder the terms:
(-8 + x) + -1ln(x + 7) = ln(x + -10) + -1ln(x + 8)

Remove parenthesis around (-8 + x)
-8 + x + -1ln(x + 7) = ln(x + -10) + -1ln(x + 8)

Reorder the terms:
-8 + x + -1ln(7 + x) = ln(x + -10) + -1ln(x + 8)
-8 + x + (7 * -1ln + x * -1ln) = ln(x + -10) + -1ln(x + 8)
-8 + x + (-7ln + -1lnx) = ln(x + -10) + -1ln(x + 8)

Reorder the terms:
-8 + -7ln + -1lnx + x = ln(x + -10) + -1ln(x + 8)

Reorder the terms:
-8 + -7ln + -1lnx + x = ln(-10 + x) + -1ln(x + 8)
-8 + -7ln + -1lnx + x = (-10 * ln + x * ln) + -1ln(x + 8)
-8 + -7ln + -1lnx + x = (-10ln + lnx) + -1ln(x + 8)

Reorder the terms:
-8 + -7ln + -1lnx + x = -10ln + lnx + -1ln(8 + x)
-8 + -7ln + -1lnx + x = -10ln + lnx + (8 * -1ln + x * -1ln)
-8 + -7ln + -1lnx + x = -10ln + lnx + (-8ln + -1lnx)

Reorder the terms:
-8 + -7ln + -1lnx + x = -10ln + -8ln + lnx + -1lnx

Combine like terms: -10ln + -8ln = -18ln
-8 + -7ln + -1lnx + x = -18ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-8 + -7ln + -1lnx + x = -18ln + 0
-8 + -7ln + -1lnx + x = -18ln

Solving
-8 + -7ln + -1lnx + x = -18ln

Solving for variable 'l'.

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

Add '18ln' to each side of the equation.
-8 + -7ln + -1lnx + 18ln + x = -18ln + 18ln

Reorder the terms:
-8 + -7ln + 18ln + -1lnx + x = -18ln + 18ln

Combine like terms: -7ln + 18ln = 11ln
-8 + 11ln + -1lnx + x = -18ln + 18ln

Combine like terms: -18ln + 18ln = 0
-8 + 11ln + -1lnx + x = 0

Add '8' to each side of the equation.
-8 + 11ln + -1lnx + 8 + x = 0 + 8

Reorder the terms:
-8 + 8 + 11ln + -1lnx + x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 11ln + -1lnx + x = 0 + 8
11ln + -1lnx + x = 0 + 8

Combine like terms: 0 + 8 = 8
11ln + -1lnx + x = 8

Add '-1x' to each side of the equation.
11ln + -1lnx + x + -1x = 8 + -1x

Combine like terms: x + -1x = 0
11ln + -1lnx + 0 = 8 + -1x
11ln + -1lnx = 8 + -1x

Reorder the terms:
-8 + 11ln + -1lnx + x = 8 + -1x + -8 + x

Reorder the terms:
-8 + 11ln + -1lnx + x = 8 + -8 + -1x + x

Combine like terms: 8 + -8 = 0
-8 + 11ln + -1lnx + x = 0 + -1x + x
-8 + 11ln + -1lnx + x = -1x + x

Combine like terms: -1x + x = 0
-8 + 11ln + -1lnx + x = 0

The solution to this equation could not be determined.

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