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Simplifying 0 = ln(x) + ln(2x + 6) Multiply ln * x 0 = lnx + ln(2x + 6) Reorder the terms: 0 = lnx + ln(6 + 2x) 0 = lnx + (6 * ln + 2x * ln) 0 = lnx + (6ln + 2lnx) Reorder the terms: 0 = 6ln + lnx + 2lnx Combine like terms: lnx + 2lnx = 3lnx 0 = 6ln + 3lnx Solving 0 = 6ln + 3lnx 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. 0 + -6ln = 6ln + -6ln + 3lnx Remove the zero: -6ln = 6ln + -6ln + 3lnx Combine like terms: 6ln + -6ln = 0 -6ln = 0 + 3lnx -6ln = 3lnx Add '-3lnx' to each side of the equation. -6ln + -3lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 -6ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), '-3ln'. -3ln(2 + x) = 0 Ignore the factor -3.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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