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Simplifying ln(2x + -6) + ln(4) = ln(37) Reorder the terms: ln(-6 + 2x) + ln(4) = ln(37) (-6 * ln + 2x * ln) + ln(4) = ln(37) (-6ln + 2lnx) + ln(4) = ln(37) Reorder the terms for easier multiplication: -6ln + 2lnx + 4ln = ln(37) Reorder the terms: -6ln + 4ln + 2lnx = ln(37) Combine like terms: -6ln + 4ln = -2ln -2ln + 2lnx = ln(37) Reorder the terms for easier multiplication: -2ln + 2lnx = 37ln Solving -2ln + 2lnx = 37ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-37ln' to each side of the equation. -2ln + -37ln + 2lnx = 37ln + -37ln Combine like terms: -2ln + -37ln = -39ln -39ln + 2lnx = 37ln + -37ln Combine like terms: 37ln + -37ln = 0 -39ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-39 + 2x) = 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 '(-39 + 2x)' equal to zero and attempt to solve: Simplifying -39 + 2x = 0 Solving -39 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '39' to each side of the equation. -39 + 39 + 2x = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 2x = 0 + 39 2x = 0 + 39 Combine like terms: 0 + 39 = 39 2x = 39 Add '-2x' to each side of the equation. 2x + -2x = 39 + -2x Combine like terms: 2x + -2x = 0 0 = 39 + -2x Simplifying 0 = 39 + -2x 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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