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

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


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

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

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

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

Solving
6ln + lnx = -4ln

Solving for variable 'l'.

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

Add '4ln' to each side of the equation.
6ln + 4ln + lnx = -4ln + 4ln

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

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

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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