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Simplifying ln(x2 + 14) + -1ln(x + 1) = ln(9x + 1) + ln(x) Reorder the terms: ln(14 + x2) + -1ln(x + 1) = ln(9x + 1) + ln(x) (14 * ln + x2 * ln) + -1ln(x + 1) = ln(9x + 1) + ln(x) (14ln + lnx2) + -1ln(x + 1) = ln(9x + 1) + ln(x) Reorder the terms: 14ln + lnx2 + -1ln(1 + x) = ln(9x + 1) + ln(x) 14ln + lnx2 + (1 * -1ln + x * -1ln) = ln(9x + 1) + ln(x) 14ln + lnx2 + (-1ln + -1lnx) = ln(9x + 1) + ln(x) Reorder the terms: 14ln + -1ln + -1lnx + lnx2 = ln(9x + 1) + ln(x) Combine like terms: 14ln + -1ln = 13ln 13ln + -1lnx + lnx2 = ln(9x + 1) + ln(x) Reorder the terms: 13ln + -1lnx + lnx2 = ln(1 + 9x) + ln(x) 13ln + -1lnx + lnx2 = (1 * ln + 9x * ln) + ln(x) 13ln + -1lnx + lnx2 = (1ln + 9lnx) + ln(x) Multiply ln * x 13ln + -1lnx + lnx2 = 1ln + 9lnx + lnx Combine like terms: 9lnx + lnx = 10lnx 13ln + -1lnx + lnx2 = 1ln + 10lnx Solving 13ln + -1lnx + lnx2 = 1ln + 10lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1ln' to each side of the equation. 13ln + -1lnx + -1ln + lnx2 = 1ln + -1ln + 10lnx Reorder the terms: 13ln + -1ln + -1lnx + lnx2 = 1ln + -1ln + 10lnx Combine like terms: 13ln + -1ln = 12ln 12ln + -1lnx + lnx2 = 1ln + -1ln + 10lnx Combine like terms: 1ln + -1ln = 0 12ln + -1lnx + lnx2 = 0 + 10lnx 12ln + -1lnx + lnx2 = 10lnx Add '-10lnx' to each side of the equation. 12ln + -1lnx + -10lnx + lnx2 = 10lnx + -10lnx Combine like terms: -1lnx + -10lnx = -11lnx 12ln + -11lnx + lnx2 = 10lnx + -10lnx Combine like terms: 10lnx + -10lnx = 0 12ln + -11lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(12 + -11x + x2) = 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 '(12 + -11x + x2)' equal to zero and attempt to solve: Simplifying 12 + -11x + x2 = 0 Solving 12 + -11x + x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -11x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -11x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -11x + x2 = 0 + -12 -11x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -11x + x2 = -12 Add '11x' to each side of the equation. -11x + 11x + x2 = -12 + 11x Combine like terms: -11x + 11x = 0 0 + x2 = -12 + 11x x2 = -12 + 11x Add '-1x2' to each side of the equation. x2 + -1x2 = -12 + 11x + -1x2 Combine like terms: x2 + -1x2 = 0 0 = -12 + 11x + -1x2 Simplifying 0 = -12 + 11x + -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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