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Simplifying 8 + -2ln(4) + -1ln(4) = 8 + -6ln(2) Reorder the terms for easier multiplication: 8 + -2 * 4ln + -1ln(4) = 8 + -6ln(2) Multiply -2 * 4 8 + -8ln + -1ln(4) = 8 + -6ln(2) Reorder the terms for easier multiplication: 8 + -8ln + -1 * 4ln = 8 + -6ln(2) Multiply -1 * 4 8 + -8ln + -4ln = 8 + -6ln(2) Combine like terms: -8ln + -4ln = -12ln 8 + -12ln = 8 + -6ln(2) Reorder the terms for easier multiplication: 8 + -12ln = 8 + -6 * 2ln Multiply -6 * 2 8 + -12ln = 8 + -12ln Add '-8' to each side of the equation. 8 + -8 + -12ln = 8 + -8 + -12ln Combine like terms: 8 + -8 = 0 0 + -12ln = 8 + -8 + -12ln -12ln = 8 + -8 + -12ln Combine like terms: 8 + -8 = 0 -12ln = 0 + -12ln -12ln = -12ln Add '12ln' to each side of the equation. -12ln + 12ln = -12ln + 12ln Combine like terms: -12ln + 12ln = 0 0 = -12ln + 12ln Combine like terms: -12ln + 12ln = 0 0 = 0 Solving 0 = 0 Couldn't find a variable to solve for. This equation is an identity, all real numbers are solutions.
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