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Simplifying ln(2x2 + -3) = ln(9x + -13) Reorder the terms: ln(-3 + 2x2) = ln(9x + -13) (-3 * ln + 2x2 * ln) = ln(9x + -13) (-3ln + 2lnx2) = ln(9x + -13) Reorder the terms: -3ln + 2lnx2 = ln(-13 + 9x) -3ln + 2lnx2 = (-13 * ln + 9x * ln) -3ln + 2lnx2 = (-13ln + 9lnx) Solving -3ln + 2lnx2 = -13ln + 9lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '13ln' to each side of the equation. -3ln + 13ln + 2lnx2 = -13ln + 13ln + 9lnx Combine like terms: -3ln + 13ln = 10ln 10ln + 2lnx2 = -13ln + 13ln + 9lnx Combine like terms: -13ln + 13ln = 0 10ln + 2lnx2 = 0 + 9lnx 10ln + 2lnx2 = 9lnx Add '-9lnx' to each side of the equation. 10ln + -9lnx + 2lnx2 = 9lnx + -9lnx Combine like terms: 9lnx + -9lnx = 0 10ln + -9lnx + 2lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(10 + -9x + 2x2) = 0 Factor a trinomial. ln((2 + -1x)(5 + -2x)) = 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 '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 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 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Add '2x' to each side of the equation. -2x + 2x = -5 + 2x Combine like terms: -2x + 2x = 0 0 = -5 + 2x Simplifying 0 = -5 + 2x 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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