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Simplifying ln(11) = ln(6x2 + -10) + -1ln(x) Reorder the terms for easier multiplication: 11ln = ln(6x2 + -10) + -1ln(x) Reorder the terms: 11ln = ln(-10 + 6x2) + -1ln(x) 11ln = (-10 * ln + 6x2 * ln) + -1ln(x) 11ln = (-10ln + 6lnx2) + -1ln(x) Multiply ln * x 11ln = -10ln + 6lnx2 + -1lnx Reorder the terms: 11ln = -10ln + -1lnx + 6lnx2 Solving 11ln = -10ln + -1lnx + 6lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '10ln' to each side of the equation. 11ln + 10ln = -10ln + -1lnx + 10ln + 6lnx2 Combine like terms: 11ln + 10ln = 21ln 21ln = -10ln + -1lnx + 10ln + 6lnx2 Reorder the terms: 21ln = -10ln + 10ln + -1lnx + 6lnx2 Combine like terms: -10ln + 10ln = 0 21ln = 0 + -1lnx + 6lnx2 21ln = -1lnx + 6lnx2 Add 'lnx' to each side of the equation. 21ln + lnx = -1lnx + lnx + 6lnx2 Combine like terms: -1lnx + lnx = 0 21ln + lnx = 0 + 6lnx2 21ln + lnx = 6lnx2 Add '-6lnx2' to each side of the equation. 21ln + lnx + -6lnx2 = 6lnx2 + -6lnx2 Combine like terms: 6lnx2 + -6lnx2 = 0 21ln + lnx + -6lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(21 + x + -6x2) = 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 '(21 + x + -6x2)' equal to zero and attempt to solve: Simplifying 21 + x + -6x2 = 0 Solving 21 + x + -6x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + x + -21 + -6x2 = 0 + -21 Reorder the terms: 21 + -21 + x + -6x2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + x + -6x2 = 0 + -21 x + -6x2 = 0 + -21 Combine like terms: 0 + -21 = -21 x + -6x2 = -21 Add '-1x' to each side of the equation. x + -1x + -6x2 = -21 + -1x Combine like terms: x + -1x = 0 0 + -6x2 = -21 + -1x -6x2 = -21 + -1x Add '6x2' to each side of the equation. -6x2 + 6x2 = -21 + -1x + 6x2 Combine like terms: -6x2 + 6x2 = 0 0 = -21 + -1x + 6x2 Simplifying 0 = -21 + -1x + 6x2 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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