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Simplifying Ln(2x + 1) + ln(3x + -5) = 1 Reorder the terms: nL(1 + 2x) + ln(3x + -5) = 1 (1 * nL + 2x * nL) + ln(3x + -5) = 1 (1nL + 2nxL) + ln(3x + -5) = 1 Reorder the terms: 1nL + 2nxL + ln(-5 + 3x) = 1 1nL + 2nxL + (-5 * ln + 3x * ln) = 1 1nL + 2nxL + (-5ln + 3lnx) = 1 Reorder the terms: -5ln + 3lnx + 1nL + 2nxL = 1 Solving -5ln + 3lnx + 1nL + 2nxL = 1 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1nL' to each side of the equation. -5ln + 3lnx + 1nL + -1nL + 2nxL = 1 + -1nL Combine like terms: 1nL + -1nL = 0 -5ln + 3lnx + 0 + 2nxL = 1 + -1nL -5ln + 3lnx + 2nxL = 1 + -1nL Add '-2nxL' to each side of the equation. -5ln + 3lnx + 2nxL + -2nxL = 1 + -1nL + -2nxL Combine like terms: 2nxL + -2nxL = 0 -5ln + 3lnx + 0 = 1 + -1nL + -2nxL -5ln + 3lnx = 1 + -1nL + -2nxL Reorder the terms: -1 + -5ln + 3lnx + nL + 2nxL = 1 + -1nL + -2nxL + -1 + nL + 2nxL Reorder the terms: -1 + -5ln + 3lnx + nL + 2nxL = 1 + -1 + -1nL + nL + -2nxL + 2nxL Combine like terms: 1 + -1 = 0 -1 + -5ln + 3lnx + nL + 2nxL = 0 + -1nL + nL + -2nxL + 2nxL -1 + -5ln + 3lnx + nL + 2nxL = -1nL + nL + -2nxL + 2nxL Combine like terms: -1nL + nL = 0 -1 + -5ln + 3lnx + nL + 2nxL = 0 + -2nxL + 2nxL -1 + -5ln + 3lnx + nL + 2nxL = -2nxL + 2nxL Combine like terms: -2nxL + 2nxL = 0 -1 + -5ln + 3lnx + nL + 2nxL = 0 The solution to this equation could not be determined.
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