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Simplifying ln(3x + -4) + ln(10x + -4) = 2ln(5x + -2) Reorder the terms: ln(-4 + 3x) + ln(10x + -4) = 2ln(5x + -2) (-4 * ln + 3x * ln) + ln(10x + -4) = 2ln(5x + -2) (-4ln + 3lnx) + ln(10x + -4) = 2ln(5x + -2) Reorder the terms: -4ln + 3lnx + ln(-4 + 10x) = 2ln(5x + -2) -4ln + 3lnx + (-4 * ln + 10x * ln) = 2ln(5x + -2) -4ln + 3lnx + (-4ln + 10lnx) = 2ln(5x + -2) Reorder the terms: -4ln + -4ln + 3lnx + 10lnx = 2ln(5x + -2) Combine like terms: -4ln + -4ln = -8ln -8ln + 3lnx + 10lnx = 2ln(5x + -2) Combine like terms: 3lnx + 10lnx = 13lnx -8ln + 13lnx = 2ln(5x + -2) Reorder the terms: -8ln + 13lnx = 2ln(-2 + 5x) -8ln + 13lnx = (-2 * 2ln + 5x * 2ln) -8ln + 13lnx = (-4ln + 10lnx) Solving -8ln + 13lnx = -4ln + 10lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '4ln' to each side of the equation. -8ln + 4ln + 13lnx = -4ln + 4ln + 10lnx Combine like terms: -8ln + 4ln = -4ln -4ln + 13lnx = -4ln + 4ln + 10lnx Combine like terms: -4ln + 4ln = 0 -4ln + 13lnx = 0 + 10lnx -4ln + 13lnx = 10lnx Add '-10lnx' to each side of the equation. -4ln + 13lnx + -10lnx = 10lnx + -10lnx Combine like terms: 13lnx + -10lnx = 3lnx -4ln + 3lnx = 10lnx + -10lnx Combine like terms: 10lnx + -10lnx = 0 -4ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-4 + 3x) = 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 '(-4 + 3x)' equal to zero and attempt to solve: Simplifying -4 + 3x = 0 Solving -4 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + 3x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 3x = 0 + 4 3x = 0 + 4 Combine like terms: 0 + 4 = 4 3x = 4 Add '-3x' to each side of the equation. 3x + -3x = 4 + -3x Combine like terms: 3x + -3x = 0 0 = 4 + -3x Simplifying 0 = 4 + -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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