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Simplifying (1 + x2) * ln(4x + 5) = 0 Reorder the terms: (1 + x2) * ln(5 + 4x) = 0 Reorder the terms for easier multiplication: ln(1 + x2)(5 + 4x) = 0 Multiply (1 + x2) * (5 + 4x) ln(1(5 + 4x) + x2(5 + 4x)) = 0 ln((5 * 1 + 4x * 1) + x2(5 + 4x)) = 0 ln((5 + 4x) + x2(5 + 4x)) = 0 ln(5 + 4x + (5 * x2 + 4x * x2)) = 0 ln(5 + 4x + (5x2 + 4x3)) = 0 ln(5 + 4x + 5x2 + 4x3) = 0 (5 * ln + 4x * ln + 5x2 * ln + 4x3 * ln) = 0 (5ln + 4lnx + 5lnx2 + 4lnx3) = 0 Solving 5ln + 4lnx + 5lnx2 + 4lnx3 = 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(5 + 4x + 5x2 + 4x3) = 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 '(5 + 4x + 5x2 + 4x3)' equal to zero and attempt to solve: Simplifying 5 + 4x + 5x2 + 4x3 = 0 Solving 5 + 4x + 5x2 + 4x3 = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + 4x + 5x2 + -5 + 4x3 = 0 + -5 Reorder the terms: 5 + -5 + 4x + 5x2 + 4x3 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4x + 5x2 + 4x3 = 0 + -5 4x + 5x2 + 4x3 = 0 + -5 Combine like terms: 0 + -5 = -5 4x + 5x2 + 4x3 = -5 Add '-4x' to each side of the equation. 4x + 5x2 + -4x + 4x3 = -5 + -4x Reorder the terms: 4x + -4x + 5x2 + 4x3 = -5 + -4x Combine like terms: 4x + -4x = 0 0 + 5x2 + 4x3 = -5 + -4x 5x2 + 4x3 = -5 + -4x Add '-5x2' to each side of the equation. 5x2 + -5x2 + 4x3 = -5 + -4x + -5x2 Combine like terms: 5x2 + -5x2 = 0 0 + 4x3 = -5 + -4x + -5x2 4x3 = -5 + -4x + -5x2 Add '-4x3' to each side of the equation. 4x3 + -4x3 = -5 + -4x + -5x2 + -4x3 Combine like terms: 4x3 + -4x3 = 0 0 = -5 + -4x + -5x2 + -4x3 Simplifying 0 = -5 + -4x + -5x2 + -4x3 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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