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

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


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

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

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

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

Combine like terms: lnx + lnx = 2lnx
4ln + 2lnx = ln(x + 6)

Reorder the terms:
4ln + 2lnx = ln(6 + x)
4ln + 2lnx = (6 * ln + x * ln)
4ln + 2lnx = (6ln + lnx)

Solving
4ln + 2lnx = 6ln + lnx

Solving for variable 'l'.

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

Add '-6ln' to each side of the equation.
4ln + -6ln + 2lnx = 6ln + -6ln + lnx

Combine like terms: 4ln + -6ln = -2ln
-2ln + 2lnx = 6ln + -6ln + lnx

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

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

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

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