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Simplifying ln(6x) = ln(x2) + -1ln(27) Remove parenthesis around (6x) ln * 6x = ln(x2) + -1ln(27) Reorder the terms for easier multiplication: 6ln * x = ln(x2) + -1ln(27) Multiply ln * x 6lnx = ln(x2) + -1ln(27) Multiply ln * x2 6lnx = lnx2 + -1ln(27) Reorder the terms for easier multiplication: 6lnx = lnx2 + -1 * 27ln Multiply -1 * 27 6lnx = lnx2 + -27ln Reorder the terms: 6lnx = -27ln + lnx2 Solving 6lnx = -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 + 6lnx = -27ln + 27ln + lnx2 Combine like terms: -27ln + 27ln = 0 27ln + 6lnx = 0 + lnx2 27ln + 6lnx = lnx2 Add '-1lnx2' to each side of the equation. 27ln + 6lnx + -1lnx2 = lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 27ln + 6lnx + -1lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(27 + 6x + -1x2) = 0 Factor a trinomial. ln((9 + -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 '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 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 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Add 'x' to each side of the equation. -1x + x = -9 + x Combine like terms: -1x + x = 0 0 = -9 + x Simplifying 0 = -9 + 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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