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Simplifying ln(5x + -2) + ln(x + 3) = ln(5x2 + 21) Reorder the terms: ln(-2 + 5x) + ln(x + 3) = ln(5x2 + 21) (-2 * ln + 5x * ln) + ln(x + 3) = ln(5x2 + 21) (-2ln + 5lnx) + ln(x + 3) = ln(5x2 + 21) Reorder the terms: -2ln + 5lnx + ln(3 + x) = ln(5x2 + 21) -2ln + 5lnx + (3 * ln + x * ln) = ln(5x2 + 21) -2ln + 5lnx + (3ln + lnx) = ln(5x2 + 21) Reorder the terms: -2ln + 3ln + 5lnx + lnx = ln(5x2 + 21) Combine like terms: -2ln + 3ln = 1ln 1ln + 5lnx + lnx = ln(5x2 + 21) Combine like terms: 5lnx + lnx = 6lnx 1ln + 6lnx = ln(5x2 + 21) Reorder the terms: 1ln + 6lnx = ln(21 + 5x2) 1ln + 6lnx = (21 * ln + 5x2 * ln) 1ln + 6lnx = (21ln + 5lnx2) Solving 1ln + 6lnx = 21ln + 5lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-21ln' to each side of the equation. 1ln + -21ln + 6lnx = 21ln + -21ln + 5lnx2 Combine like terms: 1ln + -21ln = -20ln -20ln + 6lnx = 21ln + -21ln + 5lnx2 Combine like terms: 21ln + -21ln = 0 -20ln + 6lnx = 0 + 5lnx2 -20ln + 6lnx = 5lnx2 Add '-5lnx2' to each side of the equation. -20ln + 6lnx + -5lnx2 = 5lnx2 + -5lnx2 Combine like terms: 5lnx2 + -5lnx2 = 0 -20ln + 6lnx + -5lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-20 + 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 '(-20 + 6x + -5x2)' equal to zero and attempt to solve: Simplifying -20 + 6x + -5x2 = 0 Solving -20 + 6x + -5x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 6x + 20 + -5x2 = 0 + 20 Reorder the terms: -20 + 20 + 6x + -5x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 6x + -5x2 = 0 + 20 6x + -5x2 = 0 + 20 Combine like terms: 0 + 20 = 20 6x + -5x2 = 20 Add '-6x' to each side of the equation. 6x + -6x + -5x2 = 20 + -6x Combine like terms: 6x + -6x = 0 0 + -5x2 = 20 + -6x -5x2 = 20 + -6x Add '5x2' to each side of the equation. -5x2 + 5x2 = 20 + -6x + 5x2 Combine like terms: -5x2 + 5x2 = 0 0 = 20 + -6x + 5x2 Simplifying 0 = 20 + -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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