ln(x+4)+ln(x)=ln(12)

Solution for ln(x+4)+ln(x)=ln(12) equation:

Simplifying
ln(x + 4) + ln(x) = ln(12)

Reorder the terms:
ln(4 + x) + ln(x) = ln(12)
(4 * ln + x * ln) + ln(x) = ln(12)
(4ln + lnx) + ln(x) = ln(12)

Multiply ln * x
4ln + lnx + lnx = ln(12)

Combine like terms: lnx + lnx = 2lnx
4ln + 2lnx = ln(12)

Reorder the terms for easier multiplication:
4ln + 2lnx = 12ln

Solving
4ln + 2lnx = 12ln

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.
4ln + -12ln + 2lnx = 12ln + -12ln

Combine like terms: 4ln + -12ln = -8ln
-8ln + 2lnx = 12ln + -12ln

Combine like terms: 12ln + -12ln = 0
-8ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(-4 + x) = 0

Ignore the factor 2.
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 '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 0

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

Add '4' to each side of the equation.
-4 + 4 + x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Add '-1x' to each side of the equation.
x + -1x = 4 + -1x

Combine like terms: x + -1x = 0
0 = 4 + -1x

Simplifying
0 = 4 + -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.