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Simplifying ln(x + -9) + ln(x + -2) = ln(78) Reorder the terms: ln(-9 + x) + ln(x + -2) = ln(78) (-9 * ln + x * ln) + ln(x + -2) = ln(78) (-9ln + lnx) + ln(x + -2) = ln(78) Reorder the terms: -9ln + lnx + ln(-2 + x) = ln(78) -9ln + lnx + (-2 * ln + x * ln) = ln(78) -9ln + lnx + (-2ln + lnx) = ln(78) Reorder the terms: -9ln + -2ln + lnx + lnx = ln(78) Combine like terms: -9ln + -2ln = -11ln -11ln + lnx + lnx = ln(78) Combine like terms: lnx + lnx = 2lnx -11ln + 2lnx = ln(78) Reorder the terms for easier multiplication: -11ln + 2lnx = 78ln Solving -11ln + 2lnx = 78ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-78ln' to each side of the equation. -11ln + -78ln + 2lnx = 78ln + -78ln Combine like terms: -11ln + -78ln = -89ln -89ln + 2lnx = 78ln + -78ln Combine like terms: 78ln + -78ln = 0 -89ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-89 + 2x) = 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 '(-89 + 2x)' equal to zero and attempt to solve: Simplifying -89 + 2x = 0 Solving -89 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '89' to each side of the equation. -89 + 89 + 2x = 0 + 89 Combine like terms: -89 + 89 = 0 0 + 2x = 0 + 89 2x = 0 + 89 Combine like terms: 0 + 89 = 89 2x = 89 Add '-2x' to each side of the equation. 2x + -2x = 89 + -2x Combine like terms: 2x + -2x = 0 0 = 89 + -2x Simplifying 0 = 89 + -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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