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Simplifying log[5](x + -3) = 1 + -1log[5](x + -7) Reorder the terms: glo * 5(-3 + x) = 1 + -1log[5](x + -7) Reorder the terms for easier multiplication: 5glo(-3 + x) = 1 + -1log[5](x + -7) (-3 * 5glo + x * 5glo) = 1 + -1log[5](x + -7) (-15glo + 5glox) = 1 + -1log[5](x + -7) Reorder the terms: -15glo + 5glox = 1 + -1glo * 5(-7 + x) Reorder the terms for easier multiplication: -15glo + 5glox = 1 + -1 * 5glo(-7 + x) Multiply -1 * 5 -15glo + 5glox = 1 + -5glo(-7 + x) -15glo + 5glox = 1 + (-7 * -5glo + x * -5glo) -15glo + 5glox = 1 + (35glo + -5glox) Solving -15glo + 5glox = 1 + 35glo + -5glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-35glo' to each side of the equation. -15glo + -35glo + 5glox = 1 + 35glo + -35glo + -5glox Combine like terms: -15glo + -35glo = -50glo -50glo + 5glox = 1 + 35glo + -35glo + -5glox Combine like terms: 35glo + -35glo = 0 -50glo + 5glox = 1 + 0 + -5glox -50glo + 5glox = 1 + -5glox Add '5glox' to each side of the equation. -50glo + 5glox + 5glox = 1 + -5glox + 5glox Combine like terms: 5glox + 5glox = 10glox -50glo + 10glox = 1 + -5glox + 5glox Combine like terms: -5glox + 5glox = 0 -50glo + 10glox = 1 + 0 -50glo + 10glox = 1 Reorder the terms: -1 + -50glo + 10glox = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -50glo + 10glox = 0 The solution to this equation could not be determined.
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