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Simplifying ln(14) = ln(x + -8) + -1ln(2) Reorder the terms for easier multiplication: 14ln = ln(x + -8) + -1ln(2) Reorder the terms: 14ln = ln(-8 + x) + -1ln(2) 14ln = (-8 * ln + x * ln) + -1ln(2) 14ln = (-8ln + lnx) + -1ln(2) Reorder the terms for easier multiplication: 14ln = -8ln + lnx + -1 * 2ln Multiply -1 * 2 14ln = -8ln + lnx + -2ln Reorder the terms: 14ln = -8ln + -2ln + lnx Combine like terms: -8ln + -2ln = -10ln 14ln = -10ln + lnx Solving 14ln = -10ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '10ln' to each side of the equation. 14ln + 10ln = -10ln + 10ln + lnx Combine like terms: 14ln + 10ln = 24ln 24ln = -10ln + 10ln + lnx Combine like terms: -10ln + 10ln = 0 24ln = 0 + lnx 24ln = lnx Add '-1lnx' to each side of the equation. 24ln + -1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 24ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(24 + -1x) = 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 '(24 + -1x)' equal to zero and attempt to solve: Simplifying 24 + -1x = 0 Solving 24 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + -1x = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -1x = 0 + -24 -1x = 0 + -24 Combine like terms: 0 + -24 = -24 -1x = -24 Add 'x' to each side of the equation. -1x + x = -24 + x Combine like terms: -1x + x = 0 0 = -24 + x Simplifying 0 = -24 + x 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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