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Simplifying (2x + 8) * ln(2x + 5) = 0 Reorder the terms: (8 + 2x) * ln(2x + 5) = 0 Reorder the terms: (8 + 2x) * ln(5 + 2x) = 0 Reorder the terms for easier multiplication: ln(8 + 2x)(5 + 2x) = 0 Multiply (8 + 2x) * (5 + 2x) ln(8(5 + 2x) + 2x * (5 + 2x)) = 0 ln((5 * 8 + 2x * 8) + 2x * (5 + 2x)) = 0 ln((40 + 16x) + 2x * (5 + 2x)) = 0 ln(40 + 16x + (5 * 2x + 2x * 2x)) = 0 ln(40 + 16x + (10x + 4x2)) = 0 Combine like terms: 16x + 10x = 26x ln(40 + 26x + 4x2) = 0 (40 * ln + 26x * ln + 4x2 * ln) = 0 (40ln + 26lnx + 4lnx2) = 0 Solving 40ln + 26lnx + 4lnx2 = 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), '2ln'. 2ln(20 + 13x + 2x2) = 0 Factor a trinomial. 2ln((4 + x)(5 + 2x)) = 0 Ignore the factor 2.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 '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Add '-1x' to each side of the equation. x + -1x = -4 + -1x Combine like terms: x + -1x = 0 0 = -4 + -1x Simplifying 0 = -4 + -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 '(5 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Add '-2x' to each side of the equation. 2x + -2x = -5 + -2x Combine like terms: 2x + -2x = 0 0 = -5 + -2x Simplifying 0 = -5 + -2x 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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