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