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Simplifying ln(5x + -2) + ln(x + 2) = ln(5x2 + 13) Reorder the terms: ln(-2 + 5x) + ln(x + 2) = ln(5x2 + 13) (-2 * ln + 5x * ln) + ln(x + 2) = ln(5x2 + 13) (-2ln + 5lnx) + ln(x + 2) = ln(5x2 + 13) Reorder the terms: -2ln + 5lnx + ln(2 + x) = ln(5x2 + 13) -2ln + 5lnx + (2 * ln + x * ln) = ln(5x2 + 13) -2ln + 5lnx + (2ln + lnx) = ln(5x2 + 13) Reorder the terms: -2ln + 2ln + 5lnx + lnx = ln(5x2 + 13) Combine like terms: -2ln + 2ln = 0 0 + 5lnx + lnx = ln(5x2 + 13) 5lnx + lnx = ln(5x2 + 13) Combine like terms: 5lnx + lnx = 6lnx 6lnx = ln(5x2 + 13) Reorder the terms: 6lnx = ln(13 + 5x2) 6lnx = (13 * ln + 5x2 * ln) 6lnx = (13ln + 5lnx2) Solving 6lnx = 13ln + 5lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-13ln' to each side of the equation. -13ln + 6lnx = 13ln + -13ln + 5lnx2 Combine like terms: 13ln + -13ln = 0 -13ln + 6lnx = 0 + 5lnx2 -13ln + 6lnx = 5lnx2 Add '-5lnx2' to each side of the equation. -13ln + 6lnx + -5lnx2 = 5lnx2 + -5lnx2 Combine like terms: 5lnx2 + -5lnx2 = 0 -13ln + 6lnx + -5lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-13 + 6x + -5x2) = 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 '(-13 + 6x + -5x2)' equal to zero and attempt to solve: Simplifying -13 + 6x + -5x2 = 0 Solving -13 + 6x + -5x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 6x + 13 + -5x2 = 0 + 13 Reorder the terms: -13 + 13 + 6x + -5x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 6x + -5x2 = 0 + 13 6x + -5x2 = 0 + 13 Combine like terms: 0 + 13 = 13 6x + -5x2 = 13 Add '-6x' to each side of the equation. 6x + -6x + -5x2 = 13 + -6x Combine like terms: 6x + -6x = 0 0 + -5x2 = 13 + -6x -5x2 = 13 + -6x Add '5x2' to each side of the equation. -5x2 + 5x2 = 13 + -6x + 5x2 Combine like terms: -5x2 + 5x2 = 0 0 = 13 + -6x + 5x2 Simplifying 0 = 13 + -6x + 5x2 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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