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Simplifying log(7)(3x + -5) + log(7) * 2 = 1 + log(7)(2x + -1) Reorder the terms: glo * 7(-5 + 3x) + log(7) * 2 = 1 + log(7)(2x + -1) Reorder the terms for easier multiplication: 7glo(-5 + 3x) + log(7) * 2 = 1 + log(7)(2x + -1) (-5 * 7glo + 3x * 7glo) + log(7) * 2 = 1 + log(7)(2x + -1) (-35glo + 21glox) + log(7) * 2 = 1 + log(7)(2x + -1) Reorder the terms for easier multiplication: -35glo + 21glox + 7 * 2glo = 1 + log(7)(2x + -1) Multiply 7 * 2 -35glo + 21glox + 14glo = 1 + log(7)(2x + -1) Reorder the terms: -35glo + 14glo + 21glox = 1 + log(7)(2x + -1) Combine like terms: -35glo + 14glo = -21glo -21glo + 21glox = 1 + log(7)(2x + -1) Reorder the terms: -21glo + 21glox = 1 + glo * 7(-1 + 2x) Reorder the terms for easier multiplication: -21glo + 21glox = 1 + 7glo(-1 + 2x) -21glo + 21glox = 1 + (-1 * 7glo + 2x * 7glo) -21glo + 21glox = 1 + (-7glo + 14glox) Solving -21glo + 21glox = 1 + -7glo + 14glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '7glo' to each side of the equation. -21glo + 7glo + 21glox = 1 + -7glo + 7glo + 14glox Combine like terms: -21glo + 7glo = -14glo -14glo + 21glox = 1 + -7glo + 7glo + 14glox Combine like terms: -7glo + 7glo = 0 -14glo + 21glox = 1 + 0 + 14glox -14glo + 21glox = 1 + 14glox Add '-14glox' to each side of the equation. -14glo + 21glox + -14glox = 1 + 14glox + -14glox Combine like terms: 21glox + -14glox = 7glox -14glo + 7glox = 1 + 14glox + -14glox Combine like terms: 14glox + -14glox = 0 -14glo + 7glox = 1 + 0 -14glo + 7glox = 1 Reorder the terms: -1 + -14glo + 7glox = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -14glo + 7glox = 0 The solution to this equation could not be determined.
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