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Simplifying [4ln(x + 5) + -1lnx + -1ln(x2 + -81)] = 0 Reorder the terms: [4ln(5 + x) + -1lnx + -1ln(x2 + -81)] = 0 [(5 * 4ln + x * 4ln) + -1lnx + -1ln(x2 + -81)] = 0 [(20ln + 4lnx) + -1lnx + -1ln(x2 + -81)] = 0 Reorder the terms: [20ln + 4lnx + -1lnx + -1ln(-81 + x2)] = 0 [20ln + 4lnx + -1lnx + (-81 * -1ln + x2 * -1ln)] = 0 [20ln + 4lnx + -1lnx + (81ln + -1lnx2)] = 0 Reorder the terms: [20ln + 81ln + 4lnx + -1lnx + -1lnx2] = 0 Combine like terms: 20ln + 81ln = 101ln [101ln + 4lnx + -1lnx + -1lnx2] = 0 Combine like terms: 4lnx + -1lnx = 3lnx [101ln + 3lnx + -1lnx2] = 0 Remove brackets around [101ln + 3lnx + -1lnx2] 101ln + 3lnx + -1lnx2 = 0 Solving 101ln + 3lnx + -1lnx2 = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'ln'. ln(101 + 3x + -1x2) = 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 '(101 + 3x + -1x2)' equal to zero and attempt to solve: Simplifying 101 + 3x + -1x2 = 0 Solving 101 + 3x + -1x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-101' to each side of the equation. 101 + 3x + -101 + -1x2 = 0 + -101 Reorder the terms: 101 + -101 + 3x + -1x2 = 0 + -101 Combine like terms: 101 + -101 = 0 0 + 3x + -1x2 = 0 + -101 3x + -1x2 = 0 + -101 Combine like terms: 0 + -101 = -101 3x + -1x2 = -101 Add '-3x' to each side of the equation. 3x + -3x + -1x2 = -101 + -3x Combine like terms: 3x + -3x = 0 0 + -1x2 = -101 + -3x -1x2 = -101 + -3x Add 'x2' to each side of the equation. -1x2 + x2 = -101 + -3x + x2 Combine like terms: -1x2 + x2 = 0 0 = -101 + -3x + x2 Simplifying 0 = -101 + -3x + x2 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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