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Simplifying ln(X + -3) = ln(2X + 9) Reorder the terms: ln(-3 + X) = ln(2X + 9) (-3 * ln + X * ln) = ln(2X + 9) (-3ln + lnX) = ln(2X + 9) Reorder the terms: -3ln + lnX = ln(9 + 2X) -3ln + lnX = (9 * ln + 2X * ln) -3ln + lnX = (9ln + 2lnX) Solving -3ln + lnX = 9ln + 2lnX Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-9ln' to each side of the equation. -3ln + -9ln + lnX = 9ln + -9ln + 2lnX Combine like terms: -3ln + -9ln = -12ln -12ln + lnX = 9ln + -9ln + 2lnX Combine like terms: 9ln + -9ln = 0 -12ln + lnX = 0 + 2lnX -12ln + lnX = 2lnX Add '-2lnX' to each side of the equation. -12ln + lnX + -2lnX = 2lnX + -2lnX Combine like terms: lnX + -2lnX = -1lnX -12ln + -1lnX = 2lnX + -2lnX Combine like terms: 2lnX + -2lnX = 0 -12ln + -1lnX = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(12 + X) = 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 '(12 + X)' equal to zero and attempt to solve: Simplifying 12 + X = 0 Solving 12 + X = 0 Move all terms containing l to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + X = 0 + -12 Combine like terms: 12 + -12 = 0 0 + X = 0 + -12 X = 0 + -12 Combine like terms: 0 + -12 = -12 X = -12 Add '-1X' to each side of the equation. X + -1X = -12 + -1X Combine like terms: X + -1X = 0 0 = -12 + -1X Simplifying 0 = -12 + -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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