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Simplifying ln(1 + -1x) + ln(8 + -1x) = ln(18) (1 * ln + -1x * ln) + ln(8 + -1x) = ln(18) (1ln + -1lnx) + ln(8 + -1x) = ln(18) 1ln + -1lnx + (8 * ln + -1x * ln) = ln(18) 1ln + -1lnx + (8ln + -1lnx) = ln(18) Reorder the terms: 1ln + 8ln + -1lnx + -1lnx = ln(18) Combine like terms: 1ln + 8ln = 9ln 9ln + -1lnx + -1lnx = ln(18) Combine like terms: -1lnx + -1lnx = -2lnx 9ln + -2lnx = ln(18) Reorder the terms for easier multiplication: 9ln + -2lnx = 18ln Solving 9ln + -2lnx = 18ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-18ln' to each side of the equation. 9ln + -18ln + -2lnx = 18ln + -18ln Combine like terms: 9ln + -18ln = -9ln -9ln + -2lnx = 18ln + -18ln Combine like terms: 18ln + -18ln = 0 -9ln + -2lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(9 + 2x) = 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 '(9 + 2x)' equal to zero and attempt to solve: Simplifying 9 + 2x = 0 Solving 9 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2x = 0 + -9 2x = 0 + -9 Combine like terms: 0 + -9 = -9 2x = -9 Add '-2x' to each side of the equation. 2x + -2x = -9 + -2x Combine like terms: 2x + -2x = 0 0 = -9 + -2x Simplifying 0 = -9 + -2x 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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