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

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


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

Multiply ln * x
lnx = ln(x + 6) + -1ln(x + -4)

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

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

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

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

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

Solving
lnx = 10ln

Solving for variable 'l'.

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

Add '-10ln' to each side of the equation.
-10ln + lnx = 10ln + -10ln

Combine like terms: 10ln + -10ln = 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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