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Simplifying ln(5x + -8) + -1ln(x + 2) = ln * 9 Reorder the terms: ln(-8 + 5x) + -1ln(x + 2) = ln * 9 (-8 * ln + 5x * ln) + -1ln(x + 2) = ln * 9 (-8ln + 5lnx) + -1ln(x + 2) = ln * 9 Reorder the terms: -8ln + 5lnx + -1ln(2 + x) = ln * 9 -8ln + 5lnx + (2 * -1ln + x * -1ln) = ln * 9 -8ln + 5lnx + (-2ln + -1lnx) = ln * 9 Reorder the terms: -8ln + -2ln + 5lnx + -1lnx = ln * 9 Combine like terms: -8ln + -2ln = -10ln -10ln + 5lnx + -1lnx = ln * 9 Combine like terms: 5lnx + -1lnx = 4lnx -10ln + 4lnx = ln * 9 Reorder the terms for easier multiplication: -10ln + 4lnx = 9ln Solving -10ln + 4lnx = 9ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-9ln' to each side of the equation. -10ln + -9ln + 4lnx = 9ln + -9ln Combine like terms: -10ln + -9ln = -19ln -19ln + 4lnx = 9ln + -9ln Combine like terms: 9ln + -9ln = 0 -19ln + 4lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-19 + 4x) = 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 '(-19 + 4x)' equal to zero and attempt to solve: Simplifying -19 + 4x = 0 Solving -19 + 4x = 0 Move all terms containing l to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + 4x = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 4x = 0 + 19 4x = 0 + 19 Combine like terms: 0 + 19 = 19 4x = 19 Add '-4x' to each side of the equation. 4x + -4x = 19 + -4x Combine like terms: 4x + -4x = 0 0 = 19 + -4x Simplifying 0 = 19 + -4x 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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