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Simplifying ln(12) + -1ln(5x2) = ln(x + 3) + ln(x + 2) Reorder the terms for easier multiplication: 12ln + -1ln(5x2) = ln(x + 3) + ln(x + 2) Remove parenthesis around (5x2) 12ln + -1ln * 5x2 = ln(x + 3) + ln(x + 2) Reorder the terms for easier multiplication: 12ln + -1 * 5ln * x2 = ln(x + 3) + ln(x + 2) Multiply -1 * 5 12ln + -5ln * x2 = ln(x + 3) + ln(x + 2) Multiply ln * x2 12ln + -5lnx2 = ln(x + 3) + ln(x + 2) Reorder the terms: 12ln + -5lnx2 = ln(3 + x) + ln(x + 2) 12ln + -5lnx2 = (3 * ln + x * ln) + ln(x + 2) 12ln + -5lnx2 = (3ln + lnx) + ln(x + 2) Reorder the terms: 12ln + -5lnx2 = 3ln + lnx + ln(2 + x) 12ln + -5lnx2 = 3ln + lnx + (2 * ln + x * ln) 12ln + -5lnx2 = 3ln + lnx + (2ln + lnx) Reorder the terms: 12ln + -5lnx2 = 3ln + 2ln + lnx + lnx Combine like terms: 3ln + 2ln = 5ln 12ln + -5lnx2 = 5ln + lnx + lnx Combine like terms: lnx + lnx = 2lnx 12ln + -5lnx2 = 5ln + 2lnx Solving 12ln + -5lnx2 = 5ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-5ln' to each side of the equation. 12ln + -5ln + -5lnx2 = 5ln + -5ln + 2lnx Combine like terms: 12ln + -5ln = 7ln 7ln + -5lnx2 = 5ln + -5ln + 2lnx Combine like terms: 5ln + -5ln = 0 7ln + -5lnx2 = 0 + 2lnx 7ln + -5lnx2 = 2lnx Add '-2lnx' to each side of the equation. 7ln + -2lnx + -5lnx2 = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 7ln + -2lnx + -5lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(7 + -2x + -5x2) = 0 Factor a trinomial. ln((1 + -1x)(7 + 5x)) = 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 '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Add 'x' to each side of the equation. -1x + x = -1 + x Combine like terms: -1x + x = 0 0 = -1 + x Simplifying 0 = -1 + x 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 '(7 + 5x)' equal to zero and attempt to solve: Simplifying 7 + 5x = 0 Solving 7 + 5x = 0 Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 5x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5x = 0 + -7 5x = 0 + -7 Combine like terms: 0 + -7 = -7 5x = -7 Add '-5x' to each side of the equation. 5x + -5x = -7 + -5x Combine like terms: 5x + -5x = 0 0 = -7 + -5x Simplifying 0 = -7 + -5x 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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