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Simplifying 5ln(x + 3) + -7lnx = 0 Reorder the terms: 5ln(3 + x) + -7lnx = 0 (3 * 5ln + x * 5ln) + -7lnx = 0 (15ln + 5lnx) + -7lnx = 0 Combine like terms: 5lnx + -7lnx = -2lnx 15ln + -2lnx = 0 Solving 15ln + -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), 'ln'. ln(15 + -2x) = 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 '(15 + -2x)' equal to zero and attempt to solve: Simplifying 15 + -2x = 0 Solving 15 + -2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -2x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -2x = 0 + -15 -2x = 0 + -15 Combine like terms: 0 + -15 = -15 -2x = -15 Add '2x' to each side of the equation. -2x + 2x = -15 + 2x Combine like terms: -2x + 2x = 0 0 = -15 + 2x Simplifying 0 = -15 + 2x 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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