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Simplifying ln(3x + 2) = ln(14 + -1x) Reorder the terms: ln(2 + 3x) = ln(14 + -1x) (2 * ln + 3x * ln) = ln(14 + -1x) (2ln + 3lnx) = ln(14 + -1x) 2ln + 3lnx = (14 * ln + -1x * ln) 2ln + 3lnx = (14ln + -1lnx) Solving 2ln + 3lnx = 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. 2ln + -14ln + 3lnx = 14ln + -14ln + -1lnx Combine like terms: 2ln + -14ln = -12ln -12ln + 3lnx = 14ln + -14ln + -1lnx Combine like terms: 14ln + -14ln = 0 -12ln + 3lnx = 0 + -1lnx -12ln + 3lnx = -1lnx Add 'lnx' to each side of the equation. -12ln + 3lnx + lnx = -1lnx + lnx Combine like terms: 3lnx + lnx = 4lnx -12ln + 4lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -12ln + 4lnx = 0 Factor out the Greatest Common Factor (GCF), '4ln'. 4ln(-3 + x) = 0 Ignore the factor 4.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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