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Simplifying lna + 13 = 4 + -1lna Reorder the terms: 13 + aln = 4 + -1lna Solving 13 + aln = 4 + -1aln Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add 'aln' to each side of the equation. 13 + aln + aln = 4 + -1aln + aln Combine like terms: aln + aln = 2aln 13 + 2aln = 4 + -1aln + aln Combine like terms: -1aln + aln = 0 13 + 2aln = 4 + 0 13 + 2aln = 4 Add '-13' to each side of the equation. 13 + -13 + 2aln = 4 + -13 Combine like terms: 13 + -13 = 0 0 + 2aln = 4 + -13 2aln = 4 + -13 Combine like terms: 4 + -13 = -9 2aln = -9 Divide each side by '2ln'. a = -4.5l-1n-1 Simplifying a = -4.5l-1n-1
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