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Simplifying ln(2x + 5) = ln(14 + -1x) Reorder the terms: ln(5 + 2x) = ln(14 + -1x) (5 * ln + 2x * ln) = ln(14 + -1x) (5ln + 2lnx) = ln(14 + -1x) 5ln + 2lnx = (14 * ln + -1x * ln) 5ln + 2lnx = (14ln + -1lnx) Solving 5ln + 2lnx = 14ln + -1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-14ln' to each side of the equation. 5ln + -14ln + 2lnx = 14ln + -14ln + -1lnx Combine like terms: 5ln + -14ln = -9ln -9ln + 2lnx = 14ln + -14ln + -1lnx Combine like terms: 14ln + -14ln = 0 -9ln + 2lnx = 0 + -1lnx -9ln + 2lnx = -1lnx Add 'lnx' to each side of the equation. -9ln + 2lnx + lnx = -1lnx + lnx Combine like terms: 2lnx + lnx = 3lnx -9ln + 3lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -9ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(-3 + x) = 0 Ignore the factor 3.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 '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Add '-1x' to each side of the equation. x + -1x = 3 + -1x Combine like terms: x + -1x = 0 0 = 3 + -1x Simplifying 0 = 3 + -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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