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Simplifying ln(x2 + 20) = ln(9x) Reorder the terms: ln(20 + x2) = ln(9x) (20 * ln + x2 * ln) = ln(9x) (20ln + lnx2) = ln(9x) Remove parenthesis around (9x) 20ln + lnx2 = ln * 9x Reorder the terms for easier multiplication: 20ln + lnx2 = 9ln * x Multiply ln * x 20ln + lnx2 = 9lnx Solving 20ln + lnx2 = 9lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-9lnx' to each side of the equation. 20ln + -9lnx + lnx2 = 9lnx + -9lnx Combine like terms: 9lnx + -9lnx = 0 20ln + -9lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(20 + -9x + x2) = 0 Factor a trinomial. ln((4 + -1x)(5 + -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 '(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.Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Add 'x' to each side of the equation. -1x + x = -5 + x Combine like terms: -1x + x = 0 0 = -5 + x Simplifying 0 = -5 + 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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