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Simplifying 1 = log(2x + 1) + -1log(3x + -1) Reorder the terms: 1 = glo(1 + 2x) + -1log(3x + -1) 1 = (1 * glo + 2x * glo) + -1log(3x + -1) 1 = (1glo + 2glox) + -1log(3x + -1) Reorder the terms: 1 = 1glo + 2glox + -1glo(-1 + 3x) 1 = 1glo + 2glox + (-1 * -1glo + 3x * -1glo) 1 = 1glo + 2glox + (1glo + -3glox) Reorder the terms: 1 = 1glo + 1glo + 2glox + -3glox Combine like terms: 1glo + 1glo = 2glo 1 = 2glo + 2glox + -3glox Combine like terms: 2glox + -3glox = -1glox 1 = 2glo + -1glox Solving 1 = 2glo + -1glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-2glo' to each side of the equation. 1 + -2glo = 2glo + -2glo + -1glox Combine like terms: 2glo + -2glo = 0 1 + -2glo = 0 + -1glox 1 + -2glo = -1glox Add 'glox' to each side of the equation. 1 + -2glo + glox = -1glox + glox Combine like terms: -1glox + glox = 0 1 + -2glo + glox = 0 Add '-1' to each side of the equation. 1 + -2glo + -1 + glox = 0 + -1 Reorder the terms: 1 + -1 + -2glo + glox = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2glo + glox = 0 + -1 -2glo + glox = 0 + -1 Combine like terms: 0 + -1 = -1 -2glo + glox = -1 Reorder the terms: 1 + -2glo + glox = -1 + 1 Combine like terms: -1 + 1 = 0 1 + -2glo + glox = 0 The solution to this equation could not be determined.
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