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Simplifying 5ln(x + 16) + -7lnx = 0 Reorder the terms: 5ln(16 + x) + -7lnx = 0 (16 * 5ln + x * 5ln) + -7lnx = 0 (80ln + 5lnx) + -7lnx = 0 Combine like terms: 5lnx + -7lnx = -2lnx 80ln + -2lnx = 0 Solving 80ln + -2lnx = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(40 + -1x) = 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 '(40 + -1x)' equal to zero and attempt to solve: Simplifying 40 + -1x = 0 Solving 40 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + -1x = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -1x = 0 + -40 -1x = 0 + -40 Combine like terms: 0 + -40 = -40 -1x = -40 Add 'x' to each side of the equation. -1x + x = -40 + x Combine like terms: -1x + x = 0 0 = -40 + x Simplifying 0 = -40 + 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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