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Simplifying ln(x) + ln(2x2 + 5) = 0 Multiply ln * x lnx + ln(2x2 + 5) = 0 Reorder the terms: lnx + ln(5 + 2x2) = 0 lnx + (5 * ln + 2x2 * ln) = 0 lnx + (5ln + 2lnx2) = 0 Reorder the terms: 5ln + lnx + 2lnx2 = 0 Solving 5ln + lnx + 2lnx2 = 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 + x + 2x2) = 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 + x + 2x2)' equal to zero and attempt to solve: Simplifying 5 + x + 2x2 = 0 Solving 5 + x + 2x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + x + -5 + 2x2 = 0 + -5 Reorder the terms: 5 + -5 + x + 2x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x + 2x2 = 0 + -5 x + 2x2 = 0 + -5 Combine like terms: 0 + -5 = -5 x + 2x2 = -5 Add '-1x' to each side of the equation. x + -1x + 2x2 = -5 + -1x Combine like terms: x + -1x = 0 0 + 2x2 = -5 + -1x 2x2 = -5 + -1x Add '-2x2' to each side of the equation. 2x2 + -2x2 = -5 + -1x + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 = -5 + -1x + -2x2 Simplifying 0 = -5 + -1x + -2x2 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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