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Simplifying 1 + log(3x + -1) = log(2x + -1) Reorder the terms: 1 + glo(-1 + 3x) = log(2x + -1) 1 + (-1 * glo + 3x * glo) = log(2x + -1) 1 + (-1glo + 3glox) = log(2x + -1) Reorder the terms: 1 + -1glo + 3glox = glo(-1 + 2x) 1 + -1glo + 3glox = (-1 * glo + 2x * glo) 1 + -1glo + 3glox = (-1glo + 2glox) Add 'glo' to each side of the equation. 1 + -1glo + glo + 3glox = -1glo + glo + 2glox Combine like terms: -1glo + glo = 0 1 + 0 + 3glox = -1glo + glo + 2glox 1 + 3glox = -1glo + glo + 2glox Combine like terms: -1glo + glo = 0 1 + 3glox = 0 + 2glox 1 + 3glox = 2glox Solving 1 + 3glox = 2glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-2glox' to each side of the equation. 1 + 3glox + -2glox = 2glox + -2glox Combine like terms: 3glox + -2glox = 1glox 1 + 1glox = 2glox + -2glox Combine like terms: 2glox + -2glox = 0 1 + 1glox = 0 Add '-1' to each side of the equation. 1 + -1 + 1glox = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 1glox = 0 + -1 1glox = 0 + -1 Combine like terms: 0 + -1 = -1 1glox = -1 Divide each side by '1lox'. g = -1l-1o-1x-1 Simplifying g = -1l-1o-1x-1
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