ln(5-x^2)=ln(x^2+4x-1)

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Solution for ln(5-x^2)=ln(x^2+4x-1) equation:


Simplifying
ln(5 + -1x2) = ln(x2 + 4x + -1)
(5 * ln + -1x2 * ln) = ln(x2 + 4x + -1)
(5ln + -1lnx2) = ln(x2 + 4x + -1)

Reorder the terms:
5ln + -1lnx2 = ln(-1 + 4x + x2)
5ln + -1lnx2 = (-1 * ln + 4x * ln + x2 * ln)
5ln + -1lnx2 = (-1ln + 4lnx + lnx2)

Solving
5ln + -1lnx2 = -1ln + 4lnx + lnx2

Solving for variable 'l'.

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

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

Combine like terms: 5ln + ln = 6ln
6ln + -1lnx2 = -1ln + 4lnx + ln + lnx2

Reorder the terms:
6ln + -1lnx2 = -1ln + ln + 4lnx + lnx2

Combine like terms: -1ln + ln = 0
6ln + -1lnx2 = 0 + 4lnx + lnx2
6ln + -1lnx2 = 4lnx + lnx2

Add '-4lnx' to each side of the equation.
6ln + -4lnx + -1lnx2 = 4lnx + -4lnx + lnx2

Combine like terms: 4lnx + -4lnx = 0
6ln + -4lnx + -1lnx2 = 0 + lnx2
6ln + -4lnx + -1lnx2 = lnx2

Add '-1lnx2' to each side of the equation.
6ln + -4lnx + -1lnx2 + -1lnx2 = lnx2 + -1lnx2

Combine like terms: -1lnx2 + -1lnx2 = -2lnx2
6ln + -4lnx + -2lnx2 = lnx2 + -1lnx2

Combine like terms: lnx2 + -1lnx2 = 0
6ln + -4lnx + -2lnx2 = 0

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(3 + -2x + -1x2) = 0

Factor a trinomial.
2ln((1 + -1x)(3 + x)) = 0

Ignore the factor 2.

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 '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Add '-1x' to each side of the equation. x + -1x = -3 + -1x Combine like terms: x + -1x = 0 0 = -3 + -1x Simplifying 0 = -3 + -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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