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Simplifying ln(6x2 + -15) = lnx Reorder the terms: ln(-15 + 6x2) = lnx (-15 * ln + 6x2 * ln) = lnx (-15ln + 6lnx2) = lnx Solving -15ln + 6lnx2 = lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1lnx' to each side of the equation. -15ln + -1lnx + 6lnx2 = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -15ln + -1lnx + 6lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-15 + -1x + 6x2) = 0 Factor a trinomial. ln((-3 + -2x)(5 + -3x)) = 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 '(-3 + -2x)' equal to zero and attempt to solve: Simplifying -3 + -2x = 0 Solving -3 + -2x = 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 + -2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x = 0 + 3 -2x = 0 + 3 Combine like terms: 0 + 3 = 3 -2x = 3 Add '2x' to each side of the equation. -2x + 2x = 3 + 2x Combine like terms: -2x + 2x = 0 0 = 3 + 2x Simplifying 0 = 3 + 2x 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 '(5 + -3x)' equal to zero and attempt to solve: Simplifying 5 + -3x = 0 Solving 5 + -3x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3x = 0 + -5 -3x = 0 + -5 Combine like terms: 0 + -5 = -5 -3x = -5 Add '3x' to each side of the equation. -3x + 3x = -5 + 3x Combine like terms: -3x + 3x = 0 0 = -5 + 3x Simplifying 0 = -5 + 3x 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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