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

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


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

Reorder the terms for easier multiplication:
2 * 2ln + ln(x2 + -1) = ln(4x + -1)

Multiply 2 * 2
4ln + ln(x2 + -1) = ln(4x + -1)

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

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

Reorder the terms:
3ln + lnx2 = ln(-1 + 4x)
3ln + lnx2 = (-1 * ln + 4x * ln)
3ln + lnx2 = (-1ln + 4lnx)

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

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(4 + -4x + x2) = 0

Factor a trinomial.
ln((2 + -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 '(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.

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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