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Simplifying ln(x) + ln(3x + 3) = 2ln(x + -2) Multiply ln * x lnx + ln(3x + 3) = 2ln(x + -2) Reorder the terms: lnx + ln(3 + 3x) = 2ln(x + -2) lnx + (3 * ln + 3x * ln) = 2ln(x + -2) lnx + (3ln + 3lnx) = 2ln(x + -2) Reorder the terms: 3ln + lnx + 3lnx = 2ln(x + -2) Combine like terms: lnx + 3lnx = 4lnx 3ln + 4lnx = 2ln(x + -2) Reorder the terms: 3ln + 4lnx = 2ln(-2 + x) 3ln + 4lnx = (-2 * 2ln + x * 2ln) 3ln + 4lnx = (-4ln + 2lnx) Solving 3ln + 4lnx = -4ln + 2lnx 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. 3ln + 4ln + 4lnx = -4ln + 4ln + 2lnx Combine like terms: 3ln + 4ln = 7ln 7ln + 4lnx = -4ln + 4ln + 2lnx Combine like terms: -4ln + 4ln = 0 7ln + 4lnx = 0 + 2lnx 7ln + 4lnx = 2lnx Add '-2lnx' to each side of the equation. 7ln + 4lnx + -2lnx = 2lnx + -2lnx Combine like terms: 4lnx + -2lnx = 2lnx 7ln + 2lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 7ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(7 + 2x) = 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 '(7 + 2x)' equal to zero and attempt to solve: Simplifying 7 + 2x = 0 Solving 7 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2x = 0 + -7 2x = 0 + -7 Combine like terms: 0 + -7 = -7 2x = -7 Add '-2x' to each side of the equation. 2x + -2x = -7 + -2x Combine like terms: 2x + -2x = 0 0 = -7 + -2x Simplifying 0 = -7 + -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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