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Simplifying ln(4x + 1) + ln(x2 + x) = ln(19x + -9) Reorder the terms: ln(1 + 4x) + ln(x2 + x) = ln(19x + -9) (1 * ln + 4x * ln) + ln(x2 + x) = ln(19x + -9) (1ln + 4lnx) + ln(x2 + x) = ln(19x + -9) Reorder the terms: 1ln + 4lnx + ln(x + x2) = ln(19x + -9) 1ln + 4lnx + (x * ln + x2 * ln) = ln(19x + -9) 1ln + 4lnx + (lnx + lnx2) = ln(19x + -9) Combine like terms: 4lnx + lnx = 5lnx 1ln + 5lnx + lnx2 = ln(19x + -9) Reorder the terms: 1ln + 5lnx + lnx2 = ln(-9 + 19x) 1ln + 5lnx + lnx2 = (-9 * ln + 19x * ln) 1ln + 5lnx + lnx2 = (-9ln + 19lnx) Solving 1ln + 5lnx + lnx2 = -9ln + 19lnx 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 + 5lnx + 9ln + lnx2 = -9ln + 9ln + 19lnx Reorder the terms: 1ln + 9ln + 5lnx + lnx2 = -9ln + 9ln + 19lnx Combine like terms: 1ln + 9ln = 10ln 10ln + 5lnx + lnx2 = -9ln + 9ln + 19lnx Combine like terms: -9ln + 9ln = 0 10ln + 5lnx + lnx2 = 0 + 19lnx 10ln + 5lnx + lnx2 = 19lnx Add '-19lnx' to each side of the equation. 10ln + 5lnx + -19lnx + lnx2 = 19lnx + -19lnx Combine like terms: 5lnx + -19lnx = -14lnx 10ln + -14lnx + lnx2 = 19lnx + -19lnx Combine like terms: 19lnx + -19lnx = 0 10ln + -14lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(10 + -14x + 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 '(10 + -14x + x2)' equal to zero and attempt to solve: Simplifying 10 + -14x + x2 = 0 Solving 10 + -14x + x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -14x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -14x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -14x + x2 = 0 + -10 -14x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -14x + x2 = -10 Add '14x' to each side of the equation. -14x + 14x + x2 = -10 + 14x Combine like terms: -14x + 14x = 0 0 + x2 = -10 + 14x x2 = -10 + 14x Add '-1x2' to each side of the equation. x2 + -1x2 = -10 + 14x + -1x2 Combine like terms: x2 + -1x2 = 0 0 = -10 + 14x + -1x2 Simplifying 0 = -10 + 14x + -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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