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Simplifying 2lnx = ln(2x + -3) + ln(x + -2) Reorder the terms: 2lnx = ln(-3 + 2x) + ln(x + -2) 2lnx = (-3 * ln + 2x * ln) + ln(x + -2) 2lnx = (-3ln + 2lnx) + ln(x + -2) Reorder the terms: 2lnx = -3ln + 2lnx + ln(-2 + x) 2lnx = -3ln + 2lnx + (-2 * ln + x * ln) 2lnx = -3ln + 2lnx + (-2ln + lnx) Reorder the terms: 2lnx = -3ln + -2ln + 2lnx + lnx Combine like terms: -3ln + -2ln = -5ln 2lnx = -5ln + 2lnx + lnx Combine like terms: 2lnx + lnx = 3lnx 2lnx = -5ln + 3lnx Solving 2lnx = -5ln + 3lnx 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. 5ln + 2lnx = -5ln + 5ln + 3lnx Combine like terms: -5ln + 5ln = 0 5ln + 2lnx = 0 + 3lnx 5ln + 2lnx = 3lnx Add '-3lnx' to each side of the equation. 5ln + 2lnx + -3lnx = 3lnx + -3lnx Combine like terms: 2lnx + -3lnx = -1lnx 5ln + -1lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 5ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(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 '(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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