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Simplifying (3x + -2) * ln(4) = ln(7) Reorder the terms: (-2 + 3x) * ln(4) = ln(7) Reorder the terms for easier multiplication: 4ln(-2 + 3x) = ln(7) (-2 * 4ln + 3x * 4ln) = ln(7) (-8ln + 12lnx) = ln(7) Reorder the terms for easier multiplication: -8ln + 12lnx = 7ln Solving -8ln + 12lnx = 7ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-7ln' to each side of the equation. -8ln + -7ln + 12lnx = 7ln + -7ln Combine like terms: -8ln + -7ln = -15ln -15ln + 12lnx = 7ln + -7ln Combine like terms: 7ln + -7ln = 0 -15ln + 12lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(-5 + 4x) = 0 Ignore the factor 3.Subproblem 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 '(-5 + 4x)' equal to zero and attempt to solve: Simplifying -5 + 4x = 0 Solving -5 + 4x = 0 Move all terms containing l to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 4x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 4x = 0 + 5 4x = 0 + 5 Combine like terms: 0 + 5 = 5 4x = 5 Add '-4x' to each side of the equation. 4x + -4x = 5 + -4x Combine like terms: 4x + -4x = 0 0 = 5 + -4x Simplifying 0 = 5 + -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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