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Simplifying ln(x) + ln(x + -3) = ln(2x2 + -7x + -5) Multiply ln * x lnx + ln(x + -3) = ln(2x2 + -7x + -5) Reorder the terms: lnx + ln(-3 + x) = ln(2x2 + -7x + -5) lnx + (-3 * ln + x * ln) = ln(2x2 + -7x + -5) lnx + (-3ln + lnx) = ln(2x2 + -7x + -5) Reorder the terms: -3ln + lnx + lnx = ln(2x2 + -7x + -5) Combine like terms: lnx + lnx = 2lnx -3ln + 2lnx = ln(2x2 + -7x + -5) Reorder the terms: -3ln + 2lnx = ln(-5 + -7x + 2x2) -3ln + 2lnx = (-5 * ln + -7x * ln + 2x2 * ln) -3ln + 2lnx = (-5ln + -7lnx + 2lnx2) Solving -3ln + 2lnx = -5ln + -7lnx + 2lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '5ln' to each side of the equation. -3ln + 5ln + 2lnx = -5ln + -7lnx + 5ln + 2lnx2 Combine like terms: -3ln + 5ln = 2ln 2ln + 2lnx = -5ln + -7lnx + 5ln + 2lnx2 Reorder the terms: 2ln + 2lnx = -5ln + 5ln + -7lnx + 2lnx2 Combine like terms: -5ln + 5ln = 0 2ln + 2lnx = 0 + -7lnx + 2lnx2 2ln + 2lnx = -7lnx + 2lnx2 Add '7lnx' to each side of the equation. 2ln + 2lnx + 7lnx = -7lnx + 7lnx + 2lnx2 Combine like terms: 2lnx + 7lnx = 9lnx 2ln + 9lnx = -7lnx + 7lnx + 2lnx2 Combine like terms: -7lnx + 7lnx = 0 2ln + 9lnx = 0 + 2lnx2 2ln + 9lnx = 2lnx2 Add '-2lnx2' to each side of the equation. 2ln + 9lnx + -2lnx2 = 2lnx2 + -2lnx2 Combine like terms: 2lnx2 + -2lnx2 = 0 2ln + 9lnx + -2lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(2 + 9x + -2x2) = 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 + 9x + -2x2)' equal to zero and attempt to solve: Simplifying 2 + 9x + -2x2 = 0 Solving 2 + 9x + -2x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + 9x + -2 + -2x2 = 0 + -2 Reorder the terms: 2 + -2 + 9x + -2x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 9x + -2x2 = 0 + -2 9x + -2x2 = 0 + -2 Combine like terms: 0 + -2 = -2 9x + -2x2 = -2 Add '-9x' to each side of the equation. 9x + -9x + -2x2 = -2 + -9x Combine like terms: 9x + -9x = 0 0 + -2x2 = -2 + -9x -2x2 = -2 + -9x Add '2x2' to each side of the equation. -2x2 + 2x2 = -2 + -9x + 2x2 Combine like terms: -2x2 + 2x2 = 0 0 = -2 + -9x + 2x2 Simplifying 0 = -2 + -9x + 2x2 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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