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Simplifying ln(9x) = ln(x2 + 20) Remove parenthesis around (9x) ln * 9x = ln(x2 + 20) Reorder the terms for easier multiplication: 9ln * x = ln(x2 + 20) Multiply ln * x 9lnx = ln(x2 + 20) Reorder the terms: 9lnx = ln(20 + x2) 9lnx = (20 * ln + x2 * ln) 9lnx = (20ln + lnx2) Solving 9lnx = 20ln + lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-20ln' to each side of the equation. -20ln + 9lnx = 20ln + -20ln + lnx2 Combine like terms: 20ln + -20ln = 0 -20ln + 9lnx = 0 + lnx2 -20ln + 9lnx = lnx2 Add '-1lnx2' to each side of the equation. -20ln + 9lnx + -1lnx2 = lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 -20ln + 9lnx + -1lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-20 + 9x + -1x2) = 0 Factor a trinomial. ln((-5 + x)(4 + -1x)) = 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 '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Add '-1x' to each side of the equation. x + -1x = 5 + -1x Combine like terms: x + -1x = 0 0 = 5 + -1x Simplifying 0 = 5 + -1x 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 '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Add 'x' to each side of the equation. -1x + x = -4 + x Combine like terms: -1x + x = 0 0 = -4 + x Simplifying 0 = -4 + 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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