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Simplifying ln(x + -13) = ln(2x + 9) Reorder the terms: ln(-13 + x) = ln(2x + 9) (-13 * ln + x * ln) = ln(2x + 9) (-13ln + lnx) = ln(2x + 9) Reorder the terms: -13ln + lnx = ln(9 + 2x) -13ln + lnx = (9 * ln + 2x * ln) -13ln + lnx = (9ln + 2lnx) Solving -13ln + 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. -13ln + -9ln + lnx = 9ln + -9ln + 2lnx Combine like terms: -13ln + -9ln = -22ln -22ln + lnx = 9ln + -9ln + 2lnx Combine like terms: 9ln + -9ln = 0 -22ln + lnx = 0 + 2lnx -22ln + lnx = 2lnx Add '-2lnx' to each side of the equation. -22ln + lnx + -2lnx = 2lnx + -2lnx Combine like terms: lnx + -2lnx = -1lnx -22ln + -1lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -22ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(22 + 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 '(22 + x)' equal to zero and attempt to solve: Simplifying 22 + x = 0 Solving 22 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + x = 0 + -22 Combine like terms: 22 + -22 = 0 0 + x = 0 + -22 x = 0 + -22 Combine like terms: 0 + -22 = -22 x = -22 Add '-1x' to each side of the equation. x + -1x = -22 + -1x Combine like terms: x + -1x = 0 0 = -22 + -1x Simplifying 0 = -22 + -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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