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Simplifying ln(9) = ln(x + -8) + -1ln(16) Reorder the terms for easier multiplication: 9ln = ln(x + -8) + -1ln(16) Reorder the terms: 9ln = ln(-8 + x) + -1ln(16) 9ln = (-8 * ln + x * ln) + -1ln(16) 9ln = (-8ln + lnx) + -1ln(16) Reorder the terms for easier multiplication: 9ln = -8ln + lnx + -1 * 16ln Multiply -1 * 16 9ln = -8ln + lnx + -16ln Reorder the terms: 9ln = -8ln + -16ln + lnx Combine like terms: -8ln + -16ln = -24ln 9ln = -24ln + lnx Solving 9ln = -24ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '24ln' to each side of the equation. 9ln + 24ln = -24ln + 24ln + lnx Combine like terms: 9ln + 24ln = 33ln 33ln = -24ln + 24ln + lnx Combine like terms: -24ln + 24ln = 0 33ln = 0 + lnx 33ln = lnx Add '-1lnx' to each side of the equation. 33ln + -1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 33ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(33 + -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 '(33 + -1x)' equal to zero and attempt to solve: Simplifying 33 + -1x = 0 Solving 33 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-33' to each side of the equation. 33 + -33 + -1x = 0 + -33 Combine like terms: 33 + -33 = 0 0 + -1x = 0 + -33 -1x = 0 + -33 Combine like terms: 0 + -33 = -33 -1x = -33 Add 'x' to each side of the equation. -1x + x = -33 + x Combine like terms: -1x + x = 0 0 = -33 + x Simplifying 0 = -33 + 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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