ln(x+31)-ln(3-2x)=5*ln(2)

Solution for ln(x+31)-ln(3-2x)=5*ln(2) equation:

Simplifying
ln(x + 31) + -1ln(3 + -2x) = 5ln(2)

Reorder the terms:
ln(31 + x) + -1ln(3 + -2x) = 5ln(2)
(31 * ln + x * ln) + -1ln(3 + -2x) = 5ln(2)
(31ln + lnx) + -1ln(3 + -2x) = 5ln(2)
31ln + lnx + (3 * -1ln + -2x * -1ln) = 5ln(2)
31ln + lnx + (-3ln + 2lnx) = 5ln(2)

Reorder the terms:
31ln + -3ln + lnx + 2lnx = 5ln(2)

Combine like terms: 31ln + -3ln = 28ln
28ln + lnx + 2lnx = 5ln(2)

Combine like terms: lnx + 2lnx = 3lnx
28ln + 3lnx = 5ln(2)

Reorder the terms for easier multiplication:
28ln + 3lnx = 5 * 2ln

Multiply 5 * 2
28ln + 3lnx = 10ln

Solving
28ln + 3lnx = 10ln

Solving for variable 'l'.

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

Add '-10ln' to each side of the equation.
28ln + -10ln + 3lnx = 10ln + -10ln

Combine like terms: 28ln + -10ln = 18ln
18ln + 3lnx = 10ln + -10ln

Combine like terms: 10ln + -10ln = 0
18ln + 3lnx = 0

Factor out the Greatest Common Factor (GCF), '3ln'.
3ln(6 + x) = 0

Ignore the factor 3.
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 '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Add '-1x' to each side of the equation.
x + -1x = -6 + -1x

Combine like terms: x + -1x = 0
0 = -6 + -1x

Simplifying
0 = -6 + -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.