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Simplifying ln(2 + -7x) + -2ln(x) = ln(4) (2 * ln + -7x * ln) + -2ln(x) = ln(4) (2ln + -7lnx) + -2ln(x) = ln(4) Multiply ln * x 2ln + -7lnx + -2lnx = ln(4) Combine like terms: -7lnx + -2lnx = -9lnx 2ln + -9lnx = ln(4) Reorder the terms for easier multiplication: 2ln + -9lnx = 4ln Solving 2ln + -9lnx = 4ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-4ln' to each side of the equation. 2ln + -4ln + -9lnx = 4ln + -4ln Combine like terms: 2ln + -4ln = -2ln -2ln + -9lnx = 4ln + -4ln Combine like terms: 4ln + -4ln = 0 -2ln + -9lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(2 + 9x) = 0 Ignore the factor -1.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 '(2 + 9x)' equal to zero and attempt to solve: Simplifying 2 + 9x = 0 Solving 2 + 9x = 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 + 9x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 9x = 0 + -2 9x = 0 + -2 Combine like terms: 0 + -2 = -2 9x = -2 Add '-9x' to each side of the equation. 9x + -9x = -2 + -9x Combine like terms: 9x + -9x = 0 0 = -2 + -9x Simplifying 0 = -2 + -9x 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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