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Simplifying ln(3x2 + -1x) = ln(10) Reorder the terms: ln(-1x + 3x2) = ln(10) (-1x * ln + 3x2 * ln) = ln(10) (-1lnx + 3lnx2) = ln(10) Reorder the terms for easier multiplication: -1lnx + 3lnx2 = 10ln Solving -1lnx + 3lnx2 = 10ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-10ln' to each side of the equation. -1lnx + -10ln + 3lnx2 = 10ln + -10ln Reorder the terms: -10ln + -1lnx + 3lnx2 = 10ln + -10ln Combine like terms: 10ln + -10ln = 0 -10ln + -1lnx + 3lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-10 + -1x + 3x2) = 0 Factor a trinomial. ln((-5 + -3x)(2 + -1x)) = 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 + -3x)' equal to zero and attempt to solve: Simplifying -5 + -3x = 0 Solving -5 + -3x = 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 + -3x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3x = 0 + 5 -3x = 0 + 5 Combine like terms: 0 + 5 = 5 -3x = 5 Add '3x' to each side of the equation. -3x + 3x = 5 + 3x Combine like terms: -3x + 3x = 0 0 = 5 + 3x Simplifying 0 = 5 + 3x 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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + x 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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