ln(x+2)+ln(x-1)=ln(4)

Solution for ln(x+2)+ln(x-1)=ln(4) equation:

Simplifying
ln(x + 2) + ln(x + -1) = ln(4)

Reorder the terms:
ln(2 + x) + ln(x + -1) = ln(4)
(2 * ln + x * ln) + ln(x + -1) = ln(4)
(2ln + lnx) + ln(x + -1) = ln(4)

Reorder the terms:
2ln + lnx + ln(-1 + x) = ln(4)
2ln + lnx + (-1 * ln + x * ln) = ln(4)
2ln + lnx + (-1ln + lnx) = ln(4)

Reorder the terms:
2ln + -1ln + lnx + lnx = ln(4)

Combine like terms: 2ln + -1ln = 1ln
1ln + lnx + lnx = ln(4)

Combine like terms: lnx + lnx = 2lnx
1ln + 2lnx = ln(4)

Reorder the terms for easier multiplication:
1ln + 2lnx = 4ln

Solving
1ln + 2lnx = 4ln

Solving for variable 'l'.

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

Add '-4ln' to each side of the equation.
1ln + -4ln + 2lnx = 4ln + -4ln

Combine like terms: 1ln + -4ln = -3ln
-3ln + 2lnx = 4ln + -4ln

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-3 + 2x) = 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 '(-3 + 2x)' equal to zero and attempt to solve:

Simplifying
-3 + 2x = 0

Solving
-3 + 2x = 0

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

Add '3' to each side of the equation.
-3 + 3 + 2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 2x = 0 + 3
2x = 0 + 3

Combine like terms: 0 + 3 = 3
2x = 3

Add '-2x' to each side of the equation.
2x + -2x = 3 + -2x

Combine like terms: 2x + -2x = 0
0 = 3 + -2x

Simplifying
0 = 3 + -2x

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.