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Simplifying ln(8x + 11) + -1ln(x) = ln(9) Reorder the terms: ln(11 + 8x) + -1ln(x) = ln(9) (11 * ln + 8x * ln) + -1ln(x) = ln(9) (11ln + 8lnx) + -1ln(x) = ln(9) Multiply ln * x 11ln + 8lnx + -1lnx = ln(9) Combine like terms: 8lnx + -1lnx = 7lnx 11ln + 7lnx = ln(9) Reorder the terms for easier multiplication: 11ln + 7lnx = 9ln Solving 11ln + 7lnx = 9ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-9ln' to each side of the equation. 11ln + -9ln + 7lnx = 9ln + -9ln Combine like terms: 11ln + -9ln = 2ln 2ln + 7lnx = 9ln + -9ln Combine like terms: 9ln + -9ln = 0 2ln + 7lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(2 + 7x) = 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 '(2 + 7x)' equal to zero and attempt to solve: Simplifying 2 + 7x = 0 Solving 2 + 7x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 7x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 7x = 0 + -2 7x = 0 + -2 Combine like terms: 0 + -2 = -2 7x = -2 Add '-7x' to each side of the equation. 7x + -7x = -2 + -7x Combine like terms: 7x + -7x = 0 0 = -2 + -7x Simplifying 0 = -2 + -7x 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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