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Simplifying ln(2x2 + 5) = ln(x2 + 149) Reorder the terms: ln(5 + 2x2) = ln(x2 + 149) (5 * ln + 2x2 * ln) = ln(x2 + 149) (5ln + 2lnx2) = ln(x2 + 149) Reorder the terms: 5ln + 2lnx2 = ln(149 + x2) 5ln + 2lnx2 = (149 * ln + x2 * ln) 5ln + 2lnx2 = (149ln + lnx2) Solving 5ln + 2lnx2 = 149ln + lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-149ln' to each side of the equation. 5ln + -149ln + 2lnx2 = 149ln + -149ln + lnx2 Combine like terms: 5ln + -149ln = -144ln -144ln + 2lnx2 = 149ln + -149ln + lnx2 Combine like terms: 149ln + -149ln = 0 -144ln + 2lnx2 = 0 + lnx2 -144ln + 2lnx2 = lnx2 Add '-1lnx2' to each side of the equation. -144ln + 2lnx2 + -1lnx2 = lnx2 + -1lnx2 Combine like terms: 2lnx2 + -1lnx2 = 1lnx2 -144ln + 1lnx2 = lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 -144ln + 1lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-144 + x2) = 0 Factor a difference between two squares. ln((12 + x)(-12 + 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 '(12 + x)' equal to zero and attempt to solve: Simplifying 12 + x = 0 Solving 12 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + x = 0 + -12 x = 0 + -12 Combine like terms: 0 + -12 = -12 x = -12 Add '-1x' to each side of the equation. x + -1x = -12 + -1x Combine like terms: x + -1x = 0 0 = -12 + -1x Simplifying 0 = -12 + -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 '(-12 + x)' equal to zero and attempt to solve: Simplifying -12 + x = 0 Solving -12 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + x = 0 + 12 x = 0 + 12 Combine like terms: 0 + 12 = 12 x = 12 Add '-1x' to each side of the equation. x + -1x = 12 + -1x Combine like terms: x + -1x = 0 0 = 12 + -1x Simplifying 0 = 12 + -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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