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Simplifying ln(12 + -1x) = 0.5(ln(12 + -3) + ln(12 + 3)) (12 * ln + -1x * ln) = 0.5(ln(12 + -3) + ln(12 + 3)) (12ln + -1lnx) = 0.5(ln(12 + -3) + ln(12 + 3)) Combine like terms: 12 + -3 = 9 12ln + -1lnx = 0.5(ln(9) + ln(12 + 3)) Reorder the terms for easier multiplication: 12ln + -1lnx = 0.5(9ln + ln(12 + 3)) Combine like terms: 12 + 3 = 15 12ln + -1lnx = 0.5(9ln + ln(15)) Reorder the terms for easier multiplication: 12ln + -1lnx = 0.5(9ln + 15ln) Combine like terms: 9ln + 15ln = 24ln 12ln + -1lnx = 0.5(24ln) Remove parenthesis around (24ln) 12ln + -1lnx = 0.5 * 24ln Multiply 0.5 * 24 12ln + -1lnx = 12ln Add '-12ln' to each side of the equation. 12ln + -12ln + -1lnx = 12ln + -12ln Combine like terms: 12ln + -12ln = 0 0 + -1lnx = 12ln + -12ln -1lnx = 12ln + -12ln Combine like terms: 12ln + -12ln = 0 -1lnx = 0 Solving -1lnx = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Divide each side by '-1'. lnx = 0 Simplifying lnx = 0 The solution to this equation could not be determined.
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