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Simplifying ln(x2 + 8) = ln(9x) Reorder the terms: ln(8 + x2) = ln(9x) (8 * ln + x2 * ln) = ln(9x) (8ln + lnx2) = ln(9x) Remove parenthesis around (9x) 8ln + lnx2 = ln * 9x Reorder the terms for easier multiplication: 8ln + lnx2 = 9ln * x Multiply ln * x 8ln + lnx2 = 9lnx Solving 8ln + 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. 8ln + -9lnx + lnx2 = 9lnx + -9lnx Combine like terms: 9lnx + -9lnx = 0 8ln + -9lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(8 + -9x + x2) = 0 Factor a trinomial. ln((1 + -1x)(8 + -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 '(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 '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 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 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Add 'x' to each side of the equation. -1x + x = -8 + x Combine like terms: -1x + x = 0 0 = -8 + x Simplifying 0 = -8 + 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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