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Simplifying 3ln(x + 6) = 6lnx Reorder the terms: 3ln(6 + x) = 6lnx (6 * 3ln + x * 3ln) = 6lnx (18ln + 3lnx) = 6lnx Solving 18ln + 3lnx = 6lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6lnx' to each side of the equation. 18ln + 3lnx + -6lnx = 6lnx + -6lnx Combine like terms: 3lnx + -6lnx = -3lnx 18ln + -3lnx = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 18ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(6 + -1x) = 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 '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Add 'x' to each side of the equation. -1x + x = -6 + x Combine like terms: -1x + x = 0 0 = -6 + x Simplifying 0 = -6 + x 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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