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Simplifying ln(x) = ln(15 + -1x) + -1ln(x + 1) Multiply ln * x lnx = ln(15 + -1x) + -1ln(x + 1) lnx = (15 * ln + -1x * ln) + -1ln(x + 1) lnx = (15ln + -1lnx) + -1ln(x + 1) Reorder the terms: lnx = 15ln + -1lnx + -1ln(1 + x) lnx = 15ln + -1lnx + (1 * -1ln + x * -1ln) lnx = 15ln + -1lnx + (-1ln + -1lnx) Reorder the terms: lnx = 15ln + -1ln + -1lnx + -1lnx Combine like terms: 15ln + -1ln = 14ln lnx = 14ln + -1lnx + -1lnx Combine like terms: -1lnx + -1lnx = -2lnx lnx = 14ln + -2lnx Solving lnx = 14ln + -2lnx 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. -14ln + lnx = 14ln + -14ln + -2lnx Combine like terms: 14ln + -14ln = 0 -14ln + lnx = 0 + -2lnx -14ln + lnx = -2lnx Add '2lnx' to each side of the equation. -14ln + lnx + 2lnx = -2lnx + 2lnx Combine like terms: lnx + 2lnx = 3lnx -14ln + 3lnx = -2lnx + 2lnx Combine like terms: -2lnx + 2lnx = 0 -14ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-14 + 3x) = 0Subproblem 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 '(-14 + 3x)' equal to zero and attempt to solve: Simplifying -14 + 3x = 0 Solving -14 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + 3x = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 3x = 0 + 14 3x = 0 + 14 Combine like terms: 0 + 14 = 14 3x = 14 Add '-3x' to each side of the equation. 3x + -3x = 14 + -3x Combine like terms: 3x + -3x = 0 0 = 14 + -3x Simplifying 0 = 14 + -3x 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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