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Simplifying ln(8) + -1ln(-4x) = ln(41) Reorder the terms for easier multiplication: 8ln + -1ln(-4x) = ln(41) Remove parenthesis around (-4x) 8ln + -1ln * -4x = ln(41) Reorder the terms for easier multiplication: 8ln + -1 * -4ln * x = ln(41) Multiply -1 * -4 8ln + 4ln * x = ln(41) Multiply ln * x 8ln + 4lnx = ln(41) Reorder the terms for easier multiplication: 8ln + 4lnx = 41ln Solving 8ln + 4lnx = 41ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-41ln' to each side of the equation. 8ln + -41ln + 4lnx = 41ln + -41ln Combine like terms: 8ln + -41ln = -33ln -33ln + 4lnx = 41ln + -41ln Combine like terms: 41ln + -41ln = 0 -33ln + 4lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-33 + 4x) = 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 '(-33 + 4x)' equal to zero and attempt to solve: Simplifying -33 + 4x = 0 Solving -33 + 4x = 0 Move all terms containing l to the left, all other terms to the right. Add '33' to each side of the equation. -33 + 33 + 4x = 0 + 33 Combine like terms: -33 + 33 = 0 0 + 4x = 0 + 33 4x = 0 + 33 Combine like terms: 0 + 33 = 33 4x = 33 Add '-4x' to each side of the equation. 4x + -4x = 33 + -4x Combine like terms: 4x + -4x = 0 0 = 33 + -4x Simplifying 0 = 33 + -4x 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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