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Simplifying 3ln(x + 2) = ln(x2 + 5x + 21) + ln(X) Reorder the terms: 3ln(2 + x) = ln(x2 + 5x + 21) + ln(X) (2 * 3ln + x * 3ln) = ln(x2 + 5x + 21) + ln(X) (6ln + 3lnx) = ln(x2 + 5x + 21) + ln(X) Reorder the terms: 6ln + 3lnx = ln(21 + 5x + x2) + ln(X) 6ln + 3lnx = (21 * ln + 5x * ln + x2 * ln) + ln(X) 6ln + 3lnx = (21ln + 5lnx + lnx2) + ln(X) Multiply ln * X 6ln + 3lnx = 21ln + 5lnx + lnx2 + lnX Reorder the terms: 6ln + 3lnx = 21ln + lnX + 5lnx + lnx2 Solving 6ln + 3lnx = 21ln + lnX + 5lnx + lnx2 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. 6ln + -21ln + 3lnx = 21ln + lnX + 5lnx + -21ln + lnx2 Combine like terms: 6ln + -21ln = -15ln -15ln + 3lnx = 21ln + lnX + 5lnx + -21ln + lnx2 Reorder the terms: -15ln + 3lnx = 21ln + -21ln + lnX + 5lnx + lnx2 Combine like terms: 21ln + -21ln = 0 -15ln + 3lnx = 0 + lnX + 5lnx + lnx2 -15ln + 3lnx = lnX + 5lnx + lnx2 Add '-1lnX' to each side of the equation. -15ln + -1lnX + 3lnx = lnX + 5lnx + -1lnX + lnx2 Reorder the terms: -15ln + -1lnX + 3lnx = lnX + -1lnX + 5lnx + lnx2 Combine like terms: lnX + -1lnX = 0 -15ln + -1lnX + 3lnx = 0 + 5lnx + lnx2 -15ln + -1lnX + 3lnx = 5lnx + lnx2 Add '-5lnx' to each side of the equation. -15ln + -1lnX + 3lnx + -5lnx = 5lnx + -5lnx + lnx2 Combine like terms: 3lnx + -5lnx = -2lnx -15ln + -1lnX + -2lnx = 5lnx + -5lnx + lnx2 Combine like terms: 5lnx + -5lnx = 0 -15ln + -1lnX + -2lnx = 0 + lnx2 -15ln + -1lnX + -2lnx = lnx2 Add '-1lnx2' to each side of the equation. -15ln + -1lnX + -2lnx + -1lnx2 = lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 -15ln + -1lnX + -2lnx + -1lnx2 = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(15 + X + 2x + x2) = 0 Ignore the factor -1.Subproblem 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 '(15 + X + 2x + x2)' equal to zero and attempt to solve: Simplifying 15 + X + 2x + x2 = 0 Solving 15 + X + 2x + x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + X + 2x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + X + 2x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + X + 2x + x2 = 0 + -15 X + 2x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 X + 2x + x2 = -15 Add '-1X' to each side of the equation. X + 2x + -1X + x2 = -15 + -1X Reorder the terms: X + -1X + 2x + x2 = -15 + -1X Combine like terms: X + -1X = 0 0 + 2x + x2 = -15 + -1X 2x + x2 = -15 + -1X Add '-2x' to each side of the equation. 2x + -2x + x2 = -15 + -1X + -2x Combine like terms: 2x + -2x = 0 0 + x2 = -15 + -1X + -2x x2 = -15 + -1X + -2x Add '-1x2' to each side of the equation. x2 + -1x2 = -15 + -1X + -2x + -1x2 Combine like terms: x2 + -1x2 = 0 0 = -15 + -1X + -2x + -1x2 Simplifying 0 = -15 + -1X + -2x + -1x2 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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