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Simplifying ln(5x + -3) + ln(x + 2) = ln(5x2 + 9) Reorder the terms: ln(-3 + 5x) + ln(x + 2) = ln(5x2 + 9) (-3 * ln + 5x * ln) + ln(x + 2) = ln(5x2 + 9) (-3ln + 5lnx) + ln(x + 2) = ln(5x2 + 9) Reorder the terms: -3ln + 5lnx + ln(2 + x) = ln(5x2 + 9) -3ln + 5lnx + (2 * ln + x * ln) = ln(5x2 + 9) -3ln + 5lnx + (2ln + lnx) = ln(5x2 + 9) Reorder the terms: -3ln + 2ln + 5lnx + lnx = ln(5x2 + 9) Combine like terms: -3ln + 2ln = -1ln -1ln + 5lnx + lnx = ln(5x2 + 9) Combine like terms: 5lnx + lnx = 6lnx -1ln + 6lnx = ln(5x2 + 9) Reorder the terms: -1ln + 6lnx = ln(9 + 5x2) -1ln + 6lnx = (9 * ln + 5x2 * ln) -1ln + 6lnx = (9ln + 5lnx2) Solving -1ln + 6lnx = 9ln + 5lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-9ln' to each side of the equation. -1ln + -9ln + 6lnx = 9ln + -9ln + 5lnx2 Combine like terms: -1ln + -9ln = -10ln -10ln + 6lnx = 9ln + -9ln + 5lnx2 Combine like terms: 9ln + -9ln = 0 -10ln + 6lnx = 0 + 5lnx2 -10ln + 6lnx = 5lnx2 Add '-5lnx2' to each side of the equation. -10ln + 6lnx + -5lnx2 = 5lnx2 + -5lnx2 Combine like terms: 5lnx2 + -5lnx2 = 0 -10ln + 6lnx + -5lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-10 + 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 '(-10 + 6x + -5x2)' equal to zero and attempt to solve: Simplifying -10 + 6x + -5x2 = 0 Solving -10 + 6x + -5x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 6x + 10 + -5x2 = 0 + 10 Reorder the terms: -10 + 10 + 6x + -5x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 6x + -5x2 = 0 + 10 6x + -5x2 = 0 + 10 Combine like terms: 0 + 10 = 10 6x + -5x2 = 10 Add '-6x' to each side of the equation. 6x + -6x + -5x2 = 10 + -6x Combine like terms: 6x + -6x = 0 0 + -5x2 = 10 + -6x -5x2 = 10 + -6x Add '5x2' to each side of the equation. -5x2 + 5x2 = 10 + -6x + 5x2 Combine like terms: -5x2 + 5x2 = 0 0 = 10 + -6x + 5x2 Simplifying 0 = 10 + -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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