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Simplifying ln(8(x) + 5) + -1ln(x) = ln(9) Reorder the terms: ln(5 + 8x) + -1ln(x) = ln(9) (5 * ln + 8x * ln) + -1ln(x) = ln(9) (5ln + 8lnx) + -1ln(x) = ln(9) Multiply ln * x 5ln + 8lnx + -1lnx = ln(9) Combine like terms: 8lnx + -1lnx = 7lnx 5ln + 7lnx = ln(9) Reorder the terms for easier multiplication: 5ln + 7lnx = 9ln Solving 5ln + 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. 5ln + -9ln + 7lnx = 9ln + -9ln Combine like terms: 5ln + -9ln = -4ln -4ln + 7lnx = 9ln + -9ln Combine like terms: 9ln + -9ln = 0 -4ln + 7lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-4 + 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 '(-4 + 7x)' equal to zero and attempt to solve: Simplifying -4 + 7x = 0 Solving -4 + 7x = 0 Move all terms containing l to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + 7x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 7x = 0 + 4 7x = 0 + 4 Combine like terms: 0 + 4 = 4 7x = 4 Add '-7x' to each side of the equation. 7x + -7x = 4 + -7x Combine like terms: 7x + -7x = 0 0 = 4 + -7x Simplifying 0 = 4 + -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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