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Simplifying ln(1 + -1x) + ln(2 + -1x) = ln(x + 14) (1 * ln + -1x * ln) + ln(2 + -1x) = ln(x + 14) (1ln + -1lnx) + ln(2 + -1x) = ln(x + 14) 1ln + -1lnx + (2 * ln + -1x * ln) = 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 = 3ln 3ln + -1lnx + -1lnx = ln(x + 14) Combine like terms: -1lnx + -1lnx = -2lnx 3ln + -2lnx = ln(x + 14) Reorder the terms: 3ln + -2lnx = ln(14 + x) 3ln + -2lnx = (14 * ln + x * ln) 3ln + -2lnx = (14ln + lnx) Solving 3ln + -2lnx = 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. 3ln + -14ln + -2lnx = 14ln + -14ln + lnx Combine like terms: 3ln + -14ln = -11ln -11ln + -2lnx = 14ln + -14ln + lnx Combine like terms: 14ln + -14ln = 0 -11ln + -2lnx = 0 + lnx -11ln + -2lnx = lnx Add '-1lnx' to each side of the equation. -11ln + -2lnx + -1lnx = lnx + -1lnx Combine like terms: -2lnx + -1lnx = -3lnx -11ln + -3lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -11ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(11 + 3x) = 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 '(11 + 3x)' equal to zero and attempt to solve: Simplifying 11 + 3x = 0 Solving 11 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + 3x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 3x = 0 + -11 3x = 0 + -11 Combine like terms: 0 + -11 = -11 3x = -11 Add '-3x' to each side of the equation. 3x + -3x = -11 + -3x Combine like terms: 3x + -3x = 0 0 = -11 + -3x Simplifying 0 = -11 + -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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