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Simplifying 7ln(x + 5) + -8lnx = 0 Reorder the terms: 7ln(5 + x) + -8lnx = 0 (5 * 7ln + x * 7ln) + -8lnx = 0 (35ln + 7lnx) + -8lnx = 0 Combine like terms: 7lnx + -8lnx = -1lnx 35ln + -1lnx = 0 Solving 35ln + -1lnx = 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), 'ln'. ln(35 + -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 '(35 + -1x)' equal to zero and attempt to solve: Simplifying 35 + -1x = 0 Solving 35 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + -1x = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -1x = 0 + -35 -1x = 0 + -35 Combine like terms: 0 + -35 = -35 -1x = -35 Add 'x' to each side of the equation. -1x + x = -35 + x Combine like terms: -1x + x = 0 0 = -35 + x Simplifying 0 = -35 + 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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