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Simplifying ln(4 + -2x) + ln(9 + -3x) = 21n(x + 1) (4 * ln + -2x * ln) + ln(9 + -3x) = 21n(x + 1) (4ln + -2lnx) + ln(9 + -3x) = 21n(x + 1) 4ln + -2lnx + (9 * ln + -3x * ln) = 21n(x + 1) 4ln + -2lnx + (9ln + -3lnx) = 21n(x + 1) Reorder the terms: 4ln + 9ln + -2lnx + -3lnx = 21n(x + 1) Combine like terms: 4ln + 9ln = 13ln 13ln + -2lnx + -3lnx = 21n(x + 1) Combine like terms: -2lnx + -3lnx = -5lnx 13ln + -5lnx = 21n(x + 1) Reorder the terms: 13ln + -5lnx = 21n(1 + x) 13ln + -5lnx = (1 * 21n + x * 21n) 13ln + -5lnx = (21n + 21nx) Solving 13ln + -5lnx = 21n + 21nx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Reorder the terms: 13ln + -5lnx + -21n + -21nx = 21n + -21n + 21nx + -21nx Combine like terms: 21n + -21n = 0 13ln + -5lnx + -21n + -21nx = 0 + 21nx + -21nx 13ln + -5lnx + -21n + -21nx = 21nx + -21nx Combine like terms: 21nx + -21nx = 0 13ln + -5lnx + -21n + -21nx = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(13l + -5lx + -21 + -21x) = 0Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing l to the left, all other terms to the right. Add '-1n' to each side of the equation. n + -1n = 0 + -1n Remove the zero: 0 = -1n Simplifying 0 = -1n 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 '(13l + -5lx + -21 + -21x)' equal to zero and attempt to solve: Simplifying 13l + -5lx + -21 + -21x = 0 Reorder the terms: -21 + 13l + -5lx + -21x = 0 Solving -21 + 13l + -5lx + -21x = 0 Move all terms containing l to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 13l + -5lx + 21 + -21x = 0 + 21 Reorder the terms: -21 + 21 + 13l + -5lx + -21x = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 13l + -5lx + -21x = 0 + 21 13l + -5lx + -21x = 0 + 21 Combine like terms: 0 + 21 = 21 13l + -5lx + -21x = 21 Add '21x' to each side of the equation. 13l + -5lx + -21x + 21x = 21 + 21x Combine like terms: -21x + 21x = 0 13l + -5lx + 0 = 21 + 21x 13l + -5lx = 21 + 21x 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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