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Simplifying ln(x + -4) + ln(3x + 8) = 2ln(x + 5) Reorder the terms: ln(-4 + x) + ln(3x + 8) = 2ln(x + 5) (-4 * ln + x * ln) + ln(3x + 8) = 2ln(x + 5) (-4ln + lnx) + ln(3x + 8) = 2ln(x + 5) Reorder the terms: -4ln + lnx + ln(8 + 3x) = 2ln(x + 5) -4ln + lnx + (8 * ln + 3x * ln) = 2ln(x + 5) -4ln + lnx + (8ln + 3lnx) = 2ln(x + 5) Reorder the terms: -4ln + 8ln + lnx + 3lnx = 2ln(x + 5) Combine like terms: -4ln + 8ln = 4ln 4ln + lnx + 3lnx = 2ln(x + 5) Combine like terms: lnx + 3lnx = 4lnx 4ln + 4lnx = 2ln(x + 5) Reorder the terms: 4ln + 4lnx = 2ln(5 + x) 4ln + 4lnx = (5 * 2ln + x * 2ln) 4ln + 4lnx = (10ln + 2lnx) Solving 4ln + 4lnx = 10ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-10ln' to each side of the equation. 4ln + -10ln + 4lnx = 10ln + -10ln + 2lnx Combine like terms: 4ln + -10ln = -6ln -6ln + 4lnx = 10ln + -10ln + 2lnx Combine like terms: 10ln + -10ln = 0 -6ln + 4lnx = 0 + 2lnx -6ln + 4lnx = 2lnx Add '-2lnx' to each side of the equation. -6ln + 4lnx + -2lnx = 2lnx + -2lnx Combine like terms: 4lnx + -2lnx = 2lnx -6ln + 2lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -6ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-3 + x) = 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 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 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 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Add '-1x' to each side of the equation. x + -1x = 3 + -1x Combine like terms: x + -1x = 0 0 = 3 + -1x Simplifying 0 = 3 + -1x 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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