ln(x+2)+ln(x)=ln(x+12)

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Solution for ln(x+2)+ln(x)=ln(x+12) equation: 


Simplifying
ln(x + 2) + ln(x) = ln(x + 12)

Reorder the terms:
ln(2 + x) + ln(x) = ln(x + 12)
(2 * ln + x * ln) + ln(x) = ln(x + 12)
(2ln + lnx) + ln(x) = ln(x + 12)

Multiply ln * x
2ln + lnx + lnx = ln(x + 12)

Combine like terms: lnx + lnx = 2lnx
2ln + 2lnx = ln(x + 12)

Reorder the terms:
2ln + 2lnx = ln(12 + x)
2ln + 2lnx = (12 * ln + x * ln)
2ln + 2lnx = (12ln + lnx)

Solving
2ln + 2lnx = 12ln + lnx

Solving for variable 'l'.

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

Add '-12ln' to each side of the equation.
2ln + -12ln + 2lnx = 12ln + -12ln + lnx

Combine like terms: 2ln + -12ln = -10ln
-10ln + 2lnx = 12ln + -12ln + lnx

Combine like terms: 12ln + -12ln = 0
-10ln + 2lnx = 0 + lnx
-10ln + 2lnx = lnx

Add '-1lnx' to each side of the equation.
-10ln + 2lnx + -1lnx = lnx + -1lnx

Combine like terms: 2lnx + -1lnx = 1lnx
-10ln + 1lnx = lnx + -1lnx

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