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Simplifying 7ln(x + 6) + -2ln(x) = 0 Reorder the terms: 7ln(6 + x) + -2ln(x) = 0 (6 * 7ln + x * 7ln) + -2ln(x) = 0 (42ln + 7lnx) + -2ln(x) = 0 Multiply ln * x 42ln + 7lnx + -2lnx = 0 Combine like terms: 7lnx + -2lnx = 5lnx 42ln + 5lnx = 0 Solving 42ln + 5lnx = 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(42 + 5x) = 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 '(42 + 5x)' equal to zero and attempt to solve: Simplifying 42 + 5x = 0 Solving 42 + 5x = 0 Move all terms containing l to the left, all other terms to the right. Add '-42' to each side of the equation. 42 + -42 + 5x = 0 + -42 Combine like terms: 42 + -42 = 0 0 + 5x = 0 + -42 5x = 0 + -42 Combine like terms: 0 + -42 = -42 5x = -42 Add '-5x' to each side of the equation. 5x + -5x = -42 + -5x Combine like terms: 5x + -5x = 0 0 = -42 + -5x Simplifying 0 = -42 + -5x 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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