ln(x+1)=3ln(2)-2ln(x+3)

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Solution for ln(x+1)=3ln(2)-2ln(x+3) equation: 


Simplifying
ln(x + 1) = 3ln(2) + -2ln(x + 3)

Reorder the terms:
ln(1 + x) = 3ln(2) + -2ln(x + 3)
(1 * ln + x * ln) = 3ln(2) + -2ln(x + 3)
(1ln + lnx) = 3ln(2) + -2ln(x + 3)

Reorder the terms for easier multiplication:
1ln + lnx = 3 * 2ln + -2ln(x + 3)

Multiply 3 * 2
1ln + lnx = 6ln + -2ln(x + 3)

Reorder the terms:
1ln + lnx = 6ln + -2ln(3 + x)
1ln + lnx = 6ln + (3 * -2ln + x * -2ln)
1ln + lnx = 6ln + (-6ln + -2lnx)

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

Solving
1ln + lnx = -2lnx

Solving for variable 'l'.

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

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

Combine like terms: lnx + 2lnx = 3lnx
1ln + 3lnx = -2lnx + 2lnx

Combine like terms: -2lnx + 2lnx = 0
1ln + 3lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(1 + 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 '(1 + 3x)' equal to zero and attempt to solve:

Simplifying
1 + 3x = 0

Solving
1 + 3x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3x = 0 + -1
3x = 0 + -1

Combine like terms: 0 + -1 = -1
3x = -1

Add '-3x' to each side of the equation.
3x + -3x = -1 + -3x

Combine like terms: 3x + -3x = 0
0 = -1 + -3x

Simplifying
0 = -1 + -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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