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

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


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

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

Reorder the terms:
-2ln + lnx2 = ln(-4 + 3x)
-2ln + lnx2 = (-4 * ln + 3x * ln)
-2ln + lnx2 = (-4ln + 3lnx)

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

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

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

Combine like terms: -4ln + 4ln = 0
2ln + lnx2 = 0 + 3lnx
2ln + lnx2 = 3lnx

Add '-3lnx' to each side of the equation.
2ln + -3lnx + lnx2 = 3lnx + -3lnx

Combine like terms: 3lnx + -3lnx = 0
2ln + -3lnx + lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(2 + -3x + x2) = 0

Factor a trinomial.
ln((1 + -1x)(2 + -1x)) = 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 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Add 'x' to each side of the equation. -1x + x = -1 + x Combine like terms: -1x + x = 0 0 = -1 + x Simplifying 0 = -1 + x 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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + x 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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