ln(3x-4)+ln(x+2)=ln(2x+1)+ln(x+2)

Solution for ln(3x-4)+ln(x+2)=ln(2x+1)+ln(x+2) equation:

Simplifying
ln(3x + -4) + ln(x + 2) = ln(2x + 1) + ln(x + 2)

Reorder the terms:
ln(-4 + 3x) + ln(x + 2) = ln(2x + 1) + ln(x + 2)
(-4 * ln + 3x * ln) + ln(x + 2) = ln(2x + 1) + ln(x + 2)
(-4ln + 3lnx) + ln(x + 2) = ln(2x + 1) + ln(x + 2)

Reorder the terms:
-4ln + 3lnx + ln(2 + x) = ln(2x + 1) + ln(x + 2)
-4ln + 3lnx + (2 * ln + x * ln) = ln(2x + 1) + ln(x + 2)
-4ln + 3lnx + (2ln + lnx) = ln(2x + 1) + ln(x + 2)

Reorder the terms:
-4ln + 2ln + 3lnx + lnx = ln(2x + 1) + ln(x + 2)

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

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

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

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

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

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

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

Solving
-2ln + 4lnx = 3ln + 3lnx

Solving for variable 'l'.

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

Add '-3ln' to each side of the equation.
-2ln + -3ln + 4lnx = 3ln + -3ln + 3lnx

Combine like terms: -2ln + -3ln = -5ln
-5ln + 4lnx = 3ln + -3ln + 3lnx

Combine like terms: 3ln + -3ln = 0
-5ln + 4lnx = 0 + 3lnx
-5ln + 4lnx = 3lnx

Add '-3lnx' to each side of the equation.
-5ln + 4lnx + -3lnx = 3lnx + -3lnx

Combine like terms: 4lnx + -3lnx = 1lnx
-5ln + 1lnx = 3lnx + -3lnx

Combine like terms: 3lnx + -3lnx = 0
-5ln + 1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-5 + x) = 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 '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

Add '5' to each side of the equation.
-5 + 5 + x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x = 0 + 5
x = 0 + 5

Combine like terms: 0 + 5 = 5
x = 5

Add '-1x' to each side of the equation.
x + -1x = 5 + -1x

Combine like terms: x + -1x = 0
0 = 5 + -1x

Simplifying
0 = 5 + -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.