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

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


Simplifying
ln(3x2 + -4) + ln(x2 + 1) = ln(2 + -1x2)

Reorder the terms:
ln(-4 + 3x2) + ln(x2 + 1) = ln(2 + -1x2)
(-4 * ln + 3x2 * ln) + ln(x2 + 1) = ln(2 + -1x2)
(-4ln + 3lnx2) + ln(x2 + 1) = ln(2 + -1x2)

Reorder the terms:
-4ln + 3lnx2 + ln(1 + x2) = ln(2 + -1x2)
-4ln + 3lnx2 + (1 * ln + x2 * ln) = ln(2 + -1x2)
-4ln + 3lnx2 + (1ln + lnx2) = ln(2 + -1x2)

Reorder the terms:
-4ln + 1ln + 3lnx2 + lnx2 = ln(2 + -1x2)

Combine like terms: -4ln + 1ln = -3ln
-3ln + 3lnx2 + lnx2 = ln(2 + -1x2)

Combine like terms: 3lnx2 + lnx2 = 4lnx2
-3ln + 4lnx2 = ln(2 + -1x2)
-3ln + 4lnx2 = (2 * ln + -1x2 * ln)
-3ln + 4lnx2 = (2ln + -1lnx2)

Solving
-3ln + 4lnx2 = 2ln + -1lnx2

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.
-3ln + -2ln + 4lnx2 = 2ln + -2ln + -1lnx2

Combine like terms: -3ln + -2ln = -5ln
-5ln + 4lnx2 = 2ln + -2ln + -1lnx2

Combine like terms: 2ln + -2ln = 0
-5ln + 4lnx2 = 0 + -1lnx2
-5ln + 4lnx2 = -1lnx2

Add 'lnx2' to each side of the equation.
-5ln + 4lnx2 + lnx2 = -1lnx2 + lnx2

Combine like terms: 4lnx2 + lnx2 = 5lnx2
-5ln + 5lnx2 = -1lnx2 + lnx2

Combine like terms: -1lnx2 + lnx2 = 0
-5ln + 5lnx2 = 0

Factor out the Greatest Common Factor (GCF), '5ln'.
5ln(-1 + x2) = 0

Factor a difference between two squares.
5ln((1 + x)(-1 + x)) = 0

Ignore the factor 5.

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 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 3

Set the factor '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Add '-1x' to each side of the equation. x + -1x = 1 + -1x Combine like terms: x + -1x = 0 0 = 1 + -1x Simplifying 0 = 1 + -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.

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