Ln(x+6)-ln(x+2)=ln(x)

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Solution for Ln(x+6)-ln(x+2)=ln(x) equation: 


Simplifying
Ln(x + 6) + -1ln(x + 2) = ln(x)

Reorder the terms:
nL(6 + x) + -1ln(x + 2) = ln(x)
(6 * nL + x * nL) + -1ln(x + 2) = ln(x)
(6nL + nxL) + -1ln(x + 2) = ln(x)

Reorder the terms:
6nL + nxL + -1ln(2 + x) = ln(x)
6nL + nxL + (2 * -1ln + x * -1ln) = ln(x)
6nL + nxL + (-2ln + -1lnx) = ln(x)

Reorder the terms:
-2ln + -1lnx + 6nL + nxL = ln(x)

Multiply ln * x
-2ln + -1lnx + 6nL + nxL = lnx

Solving
-2ln + -1lnx + 6nL + nxL = lnx

Solving for variable 'l'.

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

Add '-1lnx' to each side of the equation.
-2ln + -1lnx + 6nL + -1lnx + nxL = lnx + -1lnx

Reorder the terms:
-2ln + -1lnx + -1lnx + 6nL + nxL = lnx + -1lnx

Combine like terms: -1lnx + -1lnx = -2lnx
-2ln + -2lnx + 6nL + nxL = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-2ln + -2lnx + 6nL + nxL = 0

Add '-6nL' to each side of the equation.
-2ln + -2lnx + 6nL + -6nL + nxL = 0 + -6nL

Combine like terms: 6nL + -6nL = 0
-2ln + -2lnx + 0 + nxL = 0 + -6nL
-2ln + -2lnx + nxL = 0 + -6nL
Remove the zero:
-2ln + -2lnx + nxL = -6nL

Add '-1nxL' to each side of the equation.
-2ln + -2lnx + nxL + -1nxL = -6nL + -1nxL

Combine like terms: nxL + -1nxL = 0
-2ln + -2lnx + 0 = -6nL + -1nxL
-2ln + -2lnx = -6nL + -1nxL

Reorder the terms:
-2ln + -2lnx + 6nL + nxL = -6nL + 6nL + -1nxL + nxL

Combine like terms: -6nL + 6nL = 0
-2ln + -2lnx + 6nL + nxL = 0 + -1nxL + nxL
-2ln + -2lnx + 6nL + nxL = -1nxL + nxL

Combine like terms: -1nxL + nxL = 0
-2ln + -2lnx + 6nL + nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-2l + -2lx + 6L + xL) = 0


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

Simplifying
n = 0

Solving
n = 0

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

Add '-1n' to each side of the equation.
n + -1n = 0 + -1n
Remove the zero:
0 = -1n

Simplifying
0 = -1n

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 '(-2l + -2lx + 6L + xL)' equal to zero and attempt to solve:

Simplifying
-2l + -2lx + 6L + xL = 0

Reorder the terms:
6L + -2l + -2lx + xL = 0

Solving
6L + -2l + -2lx + xL = 0

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

Add '-6L' to each side of the equation.
6L + -2l + -2lx + -6L + xL = 0 + -6L

Reorder the terms:
6L + -6L + -2l + -2lx + xL = 0 + -6L

Combine like terms: 6L + -6L = 0
0 + -2l + -2lx + xL = 0 + -6L
-2l + -2lx + xL = 0 + -6L
Remove the zero:
-2l + -2lx + xL = -6L

Add '-1xL' to each side of the equation.
-2l + -2lx + xL + -1xL = -6L + -1xL

Combine like terms: xL + -1xL = 0
-2l + -2lx + 0 = -6L + -1xL
-2l + -2lx = -6L + -1xL

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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