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Simplifying ln(-5x) = ln(x2 + -14) Remove parenthesis around (-5x) ln * -5x = ln(x2 + -14) Reorder the terms for easier multiplication: -5ln * x = ln(x2 + -14) Multiply ln * x -5lnx = ln(x2 + -14) Reorder the terms: -5lnx = ln(-14 + x2) -5lnx = (-14 * ln + x2 * ln) -5lnx = (-14ln + lnx2) Solving -5lnx = -14ln + lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '14ln' to each side of the equation. 14ln + -5lnx = -14ln + 14ln + lnx2 Combine like terms: -14ln + 14ln = 0 14ln + -5lnx = 0 + lnx2 14ln + -5lnx = lnx2 Add '-1lnx2' to each side of the equation. 14ln + -5lnx + -1lnx2 = lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 14ln + -5lnx + -1lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(14 + -5x + -1x2) = 0 Factor a trinomial. ln((2 + -1x)(7 + 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 '(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 '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Add '-1x' to each side of the equation. x + -1x = -7 + -1x Combine like terms: x + -1x = 0 0 = -7 + -1x Simplifying 0 = -7 + -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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