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Simplifying ln(3x) = ln(x2 + -18) Remove parenthesis around (3x) ln * 3x = ln(x2 + -18) Reorder the terms for easier multiplication: 3ln * x = ln(x2 + -18) Multiply ln * x 3lnx = ln(x2 + -18) Reorder the terms: 3lnx = ln(-18 + x2) 3lnx = (-18 * ln + x2 * ln) 3lnx = (-18ln + lnx2) Solving 3lnx = -18ln + lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '18ln' to each side of the equation. 18ln + 3lnx = -18ln + 18ln + lnx2 Combine like terms: -18ln + 18ln = 0 18ln + 3lnx = 0 + lnx2 18ln + 3lnx = lnx2 Add '-1lnx2' to each side of the equation. 18ln + 3lnx + -1lnx2 = lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 18ln + 3lnx + -1lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(18 + 3x + -1x2) = 0 Factor a trinomial. ln((6 + -1x)(3 + x)) = 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 '(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.Subproblem 3
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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