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Simplifying ln(12x) = ln(x2 + 27) Remove parenthesis around (12x) ln * 12x = ln(x2 + 27) Reorder the terms for easier multiplication: 12ln * x = ln(x2 + 27) Multiply ln * x 12lnx = ln(x2 + 27) Reorder the terms: 12lnx = ln(27 + x2) 12lnx = (27 * ln + x2 * ln) 12lnx = (27ln + lnx2) Solving 12lnx = 27ln + lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-27ln' to each side of the equation. -27ln + 12lnx = 27ln + -27ln + lnx2 Combine like terms: 27ln + -27ln = 0 -27ln + 12lnx = 0 + lnx2 -27ln + 12lnx = lnx2 Add '-1lnx2' to each side of the equation. -27ln + 12lnx + -1lnx2 = lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 -27ln + 12lnx + -1lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-27 + 12x + -1x2) = 0 Factor a trinomial. ln((-9 + x)(3 + -1x)) = 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 '(-9 + x)' equal to zero and attempt to solve: Simplifying -9 + x = 0 Solving -9 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + x = 0 + 9 x = 0 + 9 Combine like terms: 0 + 9 = 9 x = 9 Add '-1x' to each side of the equation. x + -1x = 9 + -1x Combine like terms: x + -1x = 0 0 = 9 + -1x Simplifying 0 = 9 + -1x 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 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + 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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