ln(x^2-7)=ln(1-2x)

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Solution for ln(x^2-7)=ln(1-2x) equation:


Simplifying
ln(x2 + -7) = ln(1 + -2x)

Reorder the terms:
ln(-7 + x2) = ln(1 + -2x)
(-7 * ln + x2 * ln) = ln(1 + -2x)
(-7ln + lnx2) = ln(1 + -2x)
-7ln + lnx2 = (1 * ln + -2x * ln)
-7ln + lnx2 = (1ln + -2lnx)

Solving
-7ln + lnx2 = 1ln + -2lnx

Solving for variable 'l'.

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

Add '-1ln' to each side of the equation.
-7ln + -1ln + lnx2 = 1ln + -1ln + -2lnx

Combine like terms: -7ln + -1ln = -8ln
-8ln + lnx2 = 1ln + -1ln + -2lnx

Combine like terms: 1ln + -1ln = 0
-8ln + lnx2 = 0 + -2lnx
-8ln + lnx2 = -2lnx

Add '2lnx' to each side of the equation.
-8ln + 2lnx + lnx2 = -2lnx + 2lnx

Combine like terms: -2lnx + 2lnx = 0
-8ln + 2lnx + lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-8 + 2x + x2) = 0

Factor a trinomial.
ln((-4 + -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 '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Add 'x' to each side of the equation. -1x + x = 4 + x Combine like terms: -1x + x = 0 0 = 4 + x Simplifying 0 = 4 + 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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