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