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Simplifying ln(x2 + 8) = ln(17x) + -1ln(3) Reorder the terms: ln(8 + x2) = ln(17x) + -1ln(3) (8 * ln + x2 * ln) = ln(17x) + -1ln(3) (8ln + lnx2) = ln(17x) + -1ln(3) Remove parenthesis around (17x) 8ln + lnx2 = ln * 17x + -1ln(3) Reorder the terms for easier multiplication: 8ln + lnx2 = 17ln * x + -1ln(3) Multiply ln * x 8ln + lnx2 = 17lnx + -1ln(3) Reorder the terms for easier multiplication: 8ln + lnx2 = 17lnx + -1 * 3ln Multiply -1 * 3 8ln + lnx2 = 17lnx + -3ln Reorder the terms: 8ln + lnx2 = -3ln + 17lnx Solving 8ln + lnx2 = -3ln + 17lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '3ln' to each side of the equation. 8ln + 3ln + lnx2 = -3ln + 3ln + 17lnx Combine like terms: 8ln + 3ln = 11ln 11ln + lnx2 = -3ln + 3ln + 17lnx Combine like terms: -3ln + 3ln = 0 11ln + lnx2 = 0 + 17lnx 11ln + lnx2 = 17lnx Add '-17lnx' to each side of the equation. 11ln + -17lnx + lnx2 = 17lnx + -17lnx Combine like terms: 17lnx + -17lnx = 0 11ln + -17lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(11 + -17x + 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 '(11 + -17x + x2)' equal to zero and attempt to solve: Simplifying 11 + -17x + x2 = 0 Solving 11 + -17x + x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -17x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + -17x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -17x + x2 = 0 + -11 -17x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 -17x + x2 = -11 Add '17x' to each side of the equation. -17x + 17x + x2 = -11 + 17x Combine like terms: -17x + 17x = 0 0 + x2 = -11 + 17x x2 = -11 + 17x Add '-1x2' to each side of the equation. x2 + -1x2 = -11 + 17x + -1x2 Combine like terms: x2 + -1x2 = 0 0 = -11 + 17x + -1x2 Simplifying 0 = -11 + 17x + -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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