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Simplifying [ln(x + -2)] + [ln(x + -32)] = [6ln * 2] Reorder the terms: [ln(-2 + x)] + [ln(x + -32)] = [6ln * 2] [(-2 * ln + x * ln)] + [ln(x + -32)] = [6ln * 2] [(-2ln + lnx)] + [ln(x + -32)] = [6ln * 2] [-2ln + lnx] + [ln(x + -32)] = [6ln * 2] Remove brackets around [-2ln + lnx] -2ln + lnx + [ln(x + -32)] = [6ln * 2] Reorder the terms: -2ln + lnx + [ln(-32 + x)] = [6ln * 2] -2ln + lnx + [(-32 * ln + x * ln)] = [6ln * 2] -2ln + lnx + [(-32ln + lnx)] = [6ln * 2] -2ln + lnx + [-32ln + lnx] = [6ln * 2] Remove brackets around [-32ln + lnx] -2ln + lnx + -32ln + lnx = [6ln * 2] Reorder the terms: -2ln + -32ln + lnx + lnx = [6ln * 2] Combine like terms: -2ln + -32ln = -34ln -34ln + lnx + lnx = [6ln * 2] Combine like terms: lnx + lnx = 2lnx -34ln + 2lnx = [6ln * 2] Reorder the terms for easier multiplication: -34ln + 2lnx = [6 * 2ln] Multiply 6 * 2 -34ln + 2lnx = [12ln] Solving -34ln + 2lnx = [12ln] Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '[-12ln]' to each side of the equation. -34ln + [-12ln] + 2lnx = [12ln] + [-12ln] Combine like terms: -34ln + [-12ln] = -46ln -46ln + 2lnx = [12ln] + [-12ln] Combine like terms: [12ln] + [-12ln] = 0 -46ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-23 + x) = 0 Ignore the factor 2.Subproblem 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 '(-23 + x)' equal to zero and attempt to solve: Simplifying -23 + x = 0 Solving -23 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + x = 0 + 23 Combine like terms: -23 + 23 = 0 0 + x = 0 + 23 x = 0 + 23 Combine like terms: 0 + 23 = 23 x = 23 Add '-1x' to each side of the equation. x + -1x = 23 + -1x Combine like terms: x + -1x = 0 0 = 23 + -1x Simplifying 0 = 23 + -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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