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Simplifying ln(3x2) + -1ln(5x) = ln(x + 9) Remove parenthesis around (3x2) ln * 3x2 + -1ln(5x) = ln(x + 9) Reorder the terms for easier multiplication: 3ln * x2 + -1ln(5x) = ln(x + 9) Multiply ln * x2 3lnx2 + -1ln(5x) = ln(x + 9) Remove parenthesis around (5x) 3lnx2 + -1ln * 5x = ln(x + 9) Reorder the terms for easier multiplication: 3lnx2 + -1 * 5ln * x = ln(x + 9) Multiply -1 * 5 3lnx2 + -5ln * x = ln(x + 9) Multiply ln * x 3lnx2 + -5lnx = ln(x + 9) Reorder the terms: -5lnx + 3lnx2 = ln(x + 9) Reorder the terms: -5lnx + 3lnx2 = ln(9 + x) -5lnx + 3lnx2 = (9 * ln + x * ln) -5lnx + 3lnx2 = (9ln + lnx) Solving -5lnx + 3lnx2 = 9ln + lnx 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. -5lnx + -9ln + 3lnx2 = 9ln + -9ln + lnx Reorder the terms: -9ln + -5lnx + 3lnx2 = 9ln + -9ln + lnx Combine like terms: 9ln + -9ln = 0 -9ln + -5lnx + 3lnx2 = 0 + lnx -9ln + -5lnx + 3lnx2 = lnx Add '-1lnx' to each side of the equation. -9ln + -5lnx + -1lnx + 3lnx2 = lnx + -1lnx Combine like terms: -5lnx + -1lnx = -6lnx -9ln + -6lnx + 3lnx2 = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -9ln + -6lnx + 3lnx2 = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(-3 + -2x + x2) = 0 Factor a trinomial. 3ln((-1 + -1x)(3 + -1x)) = 0 Ignore the factor 3.Subproblem 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 '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Add 'x' to each side of the equation. -1x + x = 1 + x Combine like terms: -1x + x = 0 0 = 1 + x Simplifying 0 = 1 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + x 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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