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Simplifying ln(5x) + -1ln(x + -2) = ln(8) Remove parenthesis around (5x) ln * 5x + -1ln(x + -2) = ln(8) Reorder the terms for easier multiplication: 5ln * x + -1ln(x + -2) = ln(8) Multiply ln * x 5lnx + -1ln(x + -2) = ln(8) Reorder the terms: 5lnx + -1ln(-2 + x) = ln(8) 5lnx + (-2 * -1ln + x * -1ln) = ln(8) 5lnx + (2ln + -1lnx) = ln(8) Reorder the terms: 2ln + 5lnx + -1lnx = ln(8) Combine like terms: 5lnx + -1lnx = 4lnx 2ln + 4lnx = ln(8) Reorder the terms for easier multiplication: 2ln + 4lnx = 8ln Solving 2ln + 4lnx = 8ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-8ln' to each side of the equation. 2ln + -8ln + 4lnx = 8ln + -8ln Combine like terms: 2ln + -8ln = -6ln -6ln + 4lnx = 8ln + -8ln Combine like terms: 8ln + -8ln = 0 -6ln + 4lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-3 + 2x) = 0 Ignore the factor 2.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 '(-3 + 2x)' equal to zero and attempt to solve: Simplifying -3 + 2x = 0 Solving -3 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2x = 0 + 3 2x = 0 + 3 Combine like terms: 0 + 3 = 3 2x = 3 Add '-2x' to each side of the equation. 2x + -2x = 3 + -2x Combine like terms: 2x + -2x = 0 0 = 3 + -2x Simplifying 0 = 3 + -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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