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