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

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


Simplifying
ln(x + 6) + ln(2x) = ln(2)

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

Remove parenthesis around (2x)
6ln + lnx + ln * 2x = ln(2)

Reorder the terms for easier multiplication:
6ln + lnx + 2ln * x = ln(2)

Multiply ln * x
6ln + lnx + 2lnx = ln(2)

Combine like terms: lnx + 2lnx = 3lnx
6ln + 3lnx = ln(2)

Reorder the terms for easier multiplication:
6ln + 3lnx = 2ln

Solving
6ln + 3lnx = 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.
6ln + -2ln + 3lnx = 2ln + -2ln

Combine like terms: 6ln + -2ln = 4ln
4ln + 3lnx = 2ln + -2ln

Combine like terms: 2ln + -2ln = 0
4ln + 3lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(4 + 3x) = 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 '(4 + 3x)' equal to zero and attempt to solve:

Simplifying
4 + 3x = 0

Solving
4 + 3x = 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 + 3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3x = 0 + -4
3x = 0 + -4

Combine like terms: 0 + -4 = -4
3x = -4

Add '-3x' to each side of the equation.
3x + -3x = -4 + -3x

Combine like terms: 3x + -3x = 0
0 = -4 + -3x

Simplifying
0 = -4 + -3x

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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