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 = 2ln
lnX = 2ln + lnX + -1lnX

Combine like terms: lnX + -1lnX = 0
lnX = 2ln + 0
lnX = 2ln

Solving
lnX = 2ln

Solving for variable 'l'.

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

Add '-2ln' to each side of the equation.
-2ln + lnX = 2ln + -2ln

Combine like terms: 2ln + -2ln = 0
-2ln + lnX = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-2 + 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 '(-2 + X)' equal to zero and attempt to solve:

Simplifying
-2 + X = 0

Solving
-2 + X = 0

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

Add '2' to each side of the equation.
-2 + 2 + X = 0 + 2

Combine like terms: -2 + 2 = 0
0 + X = 0 + 2
X = 0 + 2

Combine like terms: 0 + 2 = 2
X = 2

Add '-1X' to each side of the equation.
X + -1X = 2 + -1X

Combine like terms: X + -1X = 0
0 = 2 + -1X

Simplifying
0 = 2 + -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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