ln*(x+5)=ln*(x-10)-ln*(x+1)

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Solution for ln*(x+5)=ln*(x-10)-ln*(x+1) equation: 


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

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

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

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

Reorder the terms:
5ln + lnx = -10ln + -1ln + lnx + -1lnx

Combine like terms: -10ln + -1ln = -11ln
5ln + lnx = -11ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
5ln + lnx = -11ln + 0
5ln + lnx = -11ln

Solving
5ln + lnx = -11ln

Solving for variable 'l'.

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

Add '11ln' to each side of the equation.
5ln + 11ln + lnx = -11ln + 11ln

Combine like terms: 5ln + 11ln = 16ln
16ln + lnx = -11ln + 11ln

Combine like terms: -11ln + 11ln = 0
16ln + lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(16 + x) = 0


Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve:

Simplifying
ln = 0

Solving
ln = 0

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

Simplifying
ln = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(16 + x)' equal to zero and attempt to solve:

Simplifying
16 + x = 0

Solving
16 + x = 0

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

Add '-16' to each side of the equation.
16 + -16 + x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + x = 0 + -16
x = 0 + -16

Combine like terms: 0 + -16 = -16
x = -16

Add '-1x' to each side of the equation.
x + -1x = -16 + -1x

Combine like terms: x + -1x = 0
0 = -16 + -1x

Simplifying
0 = -16 + -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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