2*ln*(y+1)=ln*(y^2-1)+ln*5

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Solution for 2*ln*(y+1)=ln*(y^2-1)+ln*5 equation:


Simplifying
2ln(y + 1) = ln(y2 + -1) + ln * 5

Reorder the terms:
2ln(1 + y) = ln(y2 + -1) + ln * 5
(1 * 2ln + y * 2ln) = ln(y2 + -1) + ln * 5
(2ln + 2lny) = ln(y2 + -1) + ln * 5

Reorder the terms:
2ln + 2lny = ln(-1 + y2) + ln * 5
2ln + 2lny = (-1 * ln + y2 * ln) + ln * 5
2ln + 2lny = (-1ln + lny2) + ln * 5

Reorder the terms for easier multiplication:
2ln + 2lny = -1ln + lny2 + 5ln

Reorder the terms:
2ln + 2lny = -1ln + 5ln + lny2

Combine like terms: -1ln + 5ln = 4ln
2ln + 2lny = 4ln + lny2

Solving
2ln + 2lny = 4ln + lny2

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 + 2lny = 4ln + -4ln + lny2

Combine like terms: 2ln + -4ln = -2ln
-2ln + 2lny = 4ln + -4ln + lny2

Combine like terms: 4ln + -4ln = 0
-2ln + 2lny = 0 + lny2
-2ln + 2lny = lny2

Add '-1lny2' to each side of the equation.
-2ln + 2lny + -1lny2 = lny2 + -1lny2

Combine like terms: lny2 + -1lny2 = 0
-2ln + 2lny + -1lny2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-2 + 2y + -1y2) = 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 '(-2 + 2y + -1y2)' equal to zero and attempt to solve: Simplifying -2 + 2y + -1y2 = 0 Solving -2 + 2y + -1y2 = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2y + 2 + -1y2 = 0 + 2 Reorder the terms: -2 + 2 + 2y + -1y2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 2y + -1y2 = 0 + 2 2y + -1y2 = 0 + 2 Combine like terms: 0 + 2 = 2 2y + -1y2 = 2 Add '-2y' to each side of the equation. 2y + -2y + -1y2 = 2 + -2y Combine like terms: 2y + -2y = 0 0 + -1y2 = 2 + -2y -1y2 = 2 + -2y Add 'y2' to each side of the equation. -1y2 + y2 = 2 + -2y + y2 Combine like terms: -1y2 + y2 = 0 0 = 2 + -2y + y2 Simplifying 0 = 2 + -2y + y2 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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