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Simplifying ln(10x + -5) = 2ln(3x + -4) Reorder the terms: ln(-5 + 10x) = 2ln(3x + -4) (-5 * ln + 10x * ln) = 2ln(3x + -4) (-5ln + 10lnx) = 2ln(3x + -4) Reorder the terms: -5ln + 10lnx = 2ln(-4 + 3x) -5ln + 10lnx = (-4 * 2ln + 3x * 2ln) -5ln + 10lnx = (-8ln + 6lnx) Solving -5ln + 10lnx = -8ln + 6lnx 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. -5ln + 8ln + 10lnx = -8ln + 8ln + 6lnx Combine like terms: -5ln + 8ln = 3ln 3ln + 10lnx = -8ln + 8ln + 6lnx Combine like terms: -8ln + 8ln = 0 3ln + 10lnx = 0 + 6lnx 3ln + 10lnx = 6lnx Add '-6lnx' to each side of the equation. 3ln + 10lnx + -6lnx = 6lnx + -6lnx Combine like terms: 10lnx + -6lnx = 4lnx 3ln + 4lnx = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 3ln + 4lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(3 + 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 '(3 + 4x)' equal to zero and attempt to solve: Simplifying 3 + 4x = 0 Solving 3 + 4x = 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 + 4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4x = 0 + -3 4x = 0 + -3 Combine like terms: 0 + -3 = -3 4x = -3 Add '-4x' to each side of the equation. 4x + -4x = -3 + -4x Combine like terms: 4x + -4x = 0 0 = -3 + -4x Simplifying 0 = -3 + -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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