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Simplifying log(7)(3x + -5) = 2 + log(7)(x + -6) Reorder the terms: glo * 7(-5 + 3x) = 2 + log(7)(x + -6) Reorder the terms for easier multiplication: 7glo(-5 + 3x) = 2 + log(7)(x + -6) (-5 * 7glo + 3x * 7glo) = 2 + log(7)(x + -6) (-35glo + 21glox) = 2 + log(7)(x + -6) Reorder the terms: -35glo + 21glox = 2 + glo * 7(-6 + x) Reorder the terms for easier multiplication: -35glo + 21glox = 2 + 7glo(-6 + x) -35glo + 21glox = 2 + (-6 * 7glo + x * 7glo) -35glo + 21glox = 2 + (-42glo + 7glox) Solving -35glo + 21glox = 2 + -42glo + 7glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '42glo' to each side of the equation. -35glo + 42glo + 21glox = 2 + -42glo + 42glo + 7glox Combine like terms: -35glo + 42glo = 7glo 7glo + 21glox = 2 + -42glo + 42glo + 7glox Combine like terms: -42glo + 42glo = 0 7glo + 21glox = 2 + 0 + 7glox 7glo + 21glox = 2 + 7glox Add '-7glox' to each side of the equation. 7glo + 21glox + -7glox = 2 + 7glox + -7glox Combine like terms: 21glox + -7glox = 14glox 7glo + 14glox = 2 + 7glox + -7glox Combine like terms: 7glox + -7glox = 0 7glo + 14glox = 2 + 0 7glo + 14glox = 2 Reorder the terms: -2 + 7glo + 14glox = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 7glo + 14glox = 0 The solution to this equation could not be determined.
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