ln(x-4)+lnx-ln(x+6)=0

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Solution for ln(x-4)+lnx-ln(x+6)=0 equation: 


Simplifying
ln(x + -4) + lnx + -1ln(x + 6) = 0

Reorder the terms:
ln(-4 + x) + lnx + -1ln(x + 6) = 0
(-4 * ln + x * ln) + lnx + -1ln(x + 6) = 0
(-4ln + lnx) + lnx + -1ln(x + 6) = 0

Reorder the terms:
-4ln + lnx + lnx + -1ln(6 + x) = 0
-4ln + lnx + lnx + (6 * -1ln + x * -1ln) = 0
-4ln + lnx + lnx + (-6ln + -1lnx) = 0

Reorder the terms:
-4ln + -6ln + lnx + lnx + -1lnx = 0

Combine like terms: -4ln + -6ln = -10ln
-10ln + lnx + lnx + -1lnx = 0

Combine like terms: lnx + lnx = 2lnx
-10ln + 2lnx + -1lnx = 0

Combine like terms: 2lnx + -1lnx = 1lnx
-10ln + 1lnx = 0

Solving
-10ln + 1lnx = 0

Solving for variable 'l'.

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-10 + 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 '(-10 + x)' equal to zero and attempt to solve:

Simplifying
-10 + x = 0

Solving
-10 + x = 0

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

Add '10' to each side of the equation.
-10 + 10 + x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + x = 0 + 10
x = 0 + 10

Combine like terms: 0 + 10 = 10
x = 10

Add '-1x' to each side of the equation.
x + -1x = 10 + -1x

Combine like terms: x + -1x = 0
0 = 10 + -1x

Simplifying
0 = 10 + -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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