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Simplifying Ln(6x + -9) + ln(4) = ln(12) + 2 Reorder the terms: nL(-9 + 6x) + ln(4) = ln(12) + 2 (-9 * nL + 6x * nL) + ln(4) = ln(12) + 2 (-9nL + 6nxL) + ln(4) = ln(12) + 2 Reorder the terms for easier multiplication: -9nL + 6nxL + 4ln = ln(12) + 2 Reorder the terms: 4ln + -9nL + 6nxL = ln(12) + 2 Reorder the terms for easier multiplication: 4ln + -9nL + 6nxL = 12ln + 2 Reorder the terms: 4ln + -9nL + 6nxL = 2 + 12ln Solving 4ln + -9nL + 6nxL = 2 + 12ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-12ln' to each side of the equation. 4ln + -9nL + -12ln + 6nxL = 2 + 12ln + -12ln Reorder the terms: 4ln + -12ln + -9nL + 6nxL = 2 + 12ln + -12ln Combine like terms: 4ln + -12ln = -8ln -8ln + -9nL + 6nxL = 2 + 12ln + -12ln Combine like terms: 12ln + -12ln = 0 -8ln + -9nL + 6nxL = 2 + 0 -8ln + -9nL + 6nxL = 2 Add '9nL' to each side of the equation. -8ln + -9nL + 9nL + 6nxL = 2 + 9nL Combine like terms: -9nL + 9nL = 0 -8ln + 0 + 6nxL = 2 + 9nL -8ln + 6nxL = 2 + 9nL Add '-6nxL' to each side of the equation. -8ln + 6nxL + -6nxL = 2 + 9nL + -6nxL Combine like terms: 6nxL + -6nxL = 0 -8ln + 0 = 2 + 9nL + -6nxL -8ln = 2 + 9nL + -6nxL Divide each side by '-8n'. l = -0.25n-1 + -1.125L + 0.75xL Simplifying l = -0.25n-1 + -1.125L + 0.75xL Reorder the terms: l = -1.125L + -0.25n-1 + 0.75xL
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