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Simplifying ln(5x + 1)(x2 + 5) = 0 Reorder the terms: ln(1 + 5x)(x2 + 5) = 0 Reorder the terms: ln(1 + 5x)(5 + x2) = 0 Multiply (1 + 5x) * (5 + x2) ln(1(5 + x2) + 5x * (5 + x2)) = 0 ln((5 * 1 + x2 * 1) + 5x * (5 + x2)) = 0 ln((5 + 1x2) + 5x * (5 + x2)) = 0 ln(5 + 1x2 + (5 * 5x + x2 * 5x)) = 0 ln(5 + 1x2 + (25x + 5x3)) = 0 Reorder the terms: ln(5 + 25x + 1x2 + 5x3) = 0 ln(5 + 25x + 1x2 + 5x3) = 0 (5 * ln + 25x * ln + 1x2 * ln + 5x3 * ln) = 0 (5ln + 25lnx + 1lnx2 + 5lnx3) = 0 Solving 5ln + 25lnx + 1lnx2 + 5lnx3 = 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 + 25x + x2 + 5x3) = 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 + 25x + x2 + 5x3)' equal to zero and attempt to solve: Simplifying 5 + 25x + x2 + 5x3 = 0 Solving 5 + 25x + x2 + 5x3 = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + 25x + x2 + -5 + 5x3 = 0 + -5 Reorder the terms: 5 + -5 + 25x + x2 + 5x3 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 25x + x2 + 5x3 = 0 + -5 25x + x2 + 5x3 = 0 + -5 Combine like terms: 0 + -5 = -5 25x + x2 + 5x3 = -5 Add '-25x' to each side of the equation. 25x + x2 + -25x + 5x3 = -5 + -25x Reorder the terms: 25x + -25x + x2 + 5x3 = -5 + -25x Combine like terms: 25x + -25x = 0 0 + x2 + 5x3 = -5 + -25x x2 + 5x3 = -5 + -25x Add '-1x2' to each side of the equation. x2 + -1x2 + 5x3 = -5 + -25x + -1x2 Combine like terms: x2 + -1x2 = 0 0 + 5x3 = -5 + -25x + -1x2 5x3 = -5 + -25x + -1x2 Add '-5x3' to each side of the equation. 5x3 + -5x3 = -5 + -25x + -1x2 + -5x3 Combine like terms: 5x3 + -5x3 = 0 0 = -5 + -25x + -1x2 + -5x3 Simplifying 0 = -5 + -25x + -1x2 + -5x3 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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