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Simplifying ln(x2 + 8x) + -1ln(x2 + -1x) = ln(2) Reorder the terms: ln(8x + x2) + -1ln(x2 + -1x) = ln(2) (8x * ln + x2 * ln) + -1ln(x2 + -1x) = ln(2) (8lnx + lnx2) + -1ln(x2 + -1x) = ln(2) Reorder the terms: 8lnx + lnx2 + -1ln(-1x + x2) = ln(2) 8lnx + lnx2 + (-1x * -1ln + x2 * -1ln) = ln(2) 8lnx + lnx2 + (1lnx + -1lnx2) = ln(2) Reorder the terms: 8lnx + 1lnx + lnx2 + -1lnx2 = ln(2) Combine like terms: 8lnx + 1lnx = 9lnx 9lnx + lnx2 + -1lnx2 = ln(2) Combine like terms: lnx2 + -1lnx2 = 0 9lnx + 0 = ln(2) 9lnx = ln(2) Reorder the terms for easier multiplication: 9lnx = 2ln Solving 9lnx = 2ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2ln' to each side of the equation. -2ln + 9lnx = 2ln + -2ln Combine like terms: 2ln + -2ln = 0 -2ln + 9lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-2 + 9x) = 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 '(-2 + 9x)' equal to zero and attempt to solve: Simplifying -2 + 9x = 0 Solving -2 + 9x = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + 9x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 9x = 0 + 2 9x = 0 + 2 Combine like terms: 0 + 2 = 2 9x = 2 Add '-9x' to each side of the equation. 9x + -9x = 2 + -9x Combine like terms: 9x + -9x = 0 0 = 2 + -9x Simplifying 0 = 2 + -9x 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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