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Simplifying ln(9x) = ln(x2 + 8) Remove parenthesis around (9x) ln * 9x = ln(x2 + 8) Reorder the terms for easier multiplication: 9ln * x = ln(x2 + 8) Multiply ln * x 9lnx = ln(x2 + 8) Reorder the terms: 9lnx = ln(8 + x2) 9lnx = (8 * ln + x2 * ln) 9lnx = (8ln + lnx2) Solving 9lnx = 8ln + lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-8ln' to each side of the equation. -8ln + 9lnx = 8ln + -8ln + lnx2 Combine like terms: 8ln + -8ln = 0 -8ln + 9lnx = 0 + lnx2 -8ln + 9lnx = lnx2 Add '-1lnx2' to each side of the equation. -8ln + 9lnx + -1lnx2 = lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 -8ln + 9lnx + -1lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-8 + 9x + -1x2) = 0 Factor a trinomial. ln((-8 + x)(1 + -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 '(-8 + x)' equal to zero and attempt to solve: Simplifying -8 + x = 0 Solving -8 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x = 0 + 8 x = 0 + 8 Combine like terms: 0 + 8 = 8 x = 8 Add '-1x' to each side of the equation. x + -1x = 8 + -1x Combine like terms: x + -1x = 0 0 = 8 + -1x Simplifying 0 = 8 + -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 '(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. The solution to this equation could not be determined.
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