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