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Simplifying ln((x + 2)(x + -2)) = ln(21) Reorder the terms: ln((2 + x)(x + -2)) = ln(21) Reorder the terms: ln((2 + x)(-2 + x)) = ln(21) Multiply (2 + x) * (-2 + x) ln((2(-2 + x) + x(-2 + x))) = ln(21) ln(((-2 * 2 + x * 2) + x(-2 + x))) = ln(21) ln(((-4 + 2x) + x(-2 + x))) = ln(21) ln((-4 + 2x + (-2 * x + x * x))) = ln(21) ln((-4 + 2x + (-2x + x2))) = ln(21) Combine like terms: 2x + -2x = 0 ln((-4 + 0 + x2)) = ln(21) ln((-4 + x2)) = ln(21) (-4 * ln + x2 * ln) = ln(21) (-4ln + lnx2) = ln(21) Reorder the terms for easier multiplication: -4ln + lnx2 = 21ln Solving -4ln + lnx2 = 21ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-21ln' to each side of the equation. -4ln + -21ln + lnx2 = 21ln + -21ln Combine like terms: -4ln + -21ln = -25ln -25ln + lnx2 = 21ln + -21ln Combine like terms: 21ln + -21ln = 0 -25ln + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-25 + x2) = 0 Factor a difference between two squares. ln((5 + x)(-5 + x)) = 0Subproblem 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 '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Add '-1x' to each side of the equation. x + -1x = -5 + -1x Combine like terms: x + -1x = 0 0 = -5 + -1x Simplifying 0 = -5 + -1x 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 '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Add '-1x' to each side of the equation. x + -1x = 5 + -1x Combine like terms: x + -1x = 0 0 = 5 + -1x Simplifying 0 = 5 + -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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