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