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