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Simplifying ln + -3x = ln(5x + 8) Reorder the terms: ln + -3x = ln(8 + 5x) ln + -3x = (8 * ln + 5x * ln) ln + -3x = (8ln + 5lnx) Solving ln + -3x = 8ln + 5lnx 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. ln + -8ln + -3x = 8ln + -8ln + 5lnx Combine like terms: ln + -8ln = -7ln -7ln + -3x = 8ln + -8ln + 5lnx Combine like terms: 8ln + -8ln = 0 -7ln + -3x = 0 + 5lnx -7ln + -3x = 5lnx Add '-5lnx' to each side of the equation. -7ln + -5lnx + -3x = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 -7ln + -5lnx + -3x = 0 Add '3x' to each side of the equation. -7ln + -5lnx + -3x + 3x = 0 + 3x Combine like terms: -3x + 3x = 0 -7ln + -5lnx + 0 = 0 + 3x -7ln + -5lnx = 0 + 3x Remove the zero: -7ln + -5lnx = 3x Combine like terms: 3x + -3x = 0 -7ln + -5lnx + -3x = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(7ln + 5lnx + 3x) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7ln + 5lnx + 3x)' equal to zero and attempt to solve: Simplifying 7ln + 5lnx + 3x = 0 Solving 7ln + 5lnx + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3x' to each side of the equation. 7ln + 5lnx + 3x + -3x = 0 + -3x Combine like terms: 3x + -3x = 0 7ln + 5lnx + 0 = 0 + -3x 7ln + 5lnx = 0 + -3x Remove the zero: 7ln + 5lnx = -3x 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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