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Simplifying ln(x + -6) + lb(x + -3) = ln(x + 2) Reorder the terms: ln(-6 + x) + lb(x + -3) = ln(x + 2) (-6 * ln + x * ln) + lb(x + -3) = ln(x + 2) (-6ln + lnx) + lb(x + -3) = ln(x + 2) Reorder the terms: -6ln + lnx + bl(-3 + x) = ln(x + 2) -6ln + lnx + (-3 * bl + x * bl) = ln(x + 2) -6ln + lnx + (-3bl + blx) = ln(x + 2) Reorder the terms: -3bl + blx + -6ln + lnx = ln(x + 2) Reorder the terms: -3bl + blx + -6ln + lnx = ln(2 + x) -3bl + blx + -6ln + lnx = (2 * ln + x * ln) -3bl + blx + -6ln + lnx = (2ln + lnx) Add '-1lnx' to each side of the equation. -3bl + blx + -6ln + lnx + -1lnx = 2ln + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -3bl + blx + -6ln + 0 = 2ln + lnx + -1lnx -3bl + blx + -6ln = 2ln + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -3bl + blx + -6ln = 2ln + 0 -3bl + blx + -6ln = 2ln Solving -3bl + blx + -6ln = 2ln Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '6ln' to each side of the equation. -3bl + blx + -6ln + 6ln = 2ln + 6ln Combine like terms: -6ln + 6ln = 0 -3bl + blx + 0 = 2ln + 6ln -3bl + blx = 2ln + 6ln Combine like terms: 2ln + 6ln = 8ln -3bl + blx = 8ln Combine like terms: 8ln + -8ln = 0 -3bl + blx + -8ln = 0 Factor out the Greatest Common Factor (GCF), 'l'. l(-3b + bx + -8n) = 0Subproblem 1
Set the factor 'l' equal to zero and attempt to solve: Simplifying l = 0 Solving l = 0 Move all terms containing b to the left, all other terms to the right. Add '-1l' to each side of the equation. l + -1l = 0 + -1l Remove the zero: 0 = -1l Simplifying 0 = -1l 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 '(-3b + bx + -8n)' equal to zero and attempt to solve: Simplifying -3b + bx + -8n = 0 Solving -3b + bx + -8n = 0 Move all terms containing b to the left, all other terms to the right. Add '8n' to each side of the equation. -3b + bx + -8n + 8n = 0 + 8n Combine like terms: -8n + 8n = 0 -3b + bx + 0 = 0 + 8n -3b + bx = 0 + 8n Remove the zero: -3b + bx = 8n 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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