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Simplifying log[5](x + -1) + -1log[5](x + 4) = log[5](x + -5) Reorder the terms: glo * 5(-1 + x) + -1log[5](x + 4) = log[5](x + -5) Reorder the terms for easier multiplication: 5glo(-1 + x) + -1log[5](x + 4) = log[5](x + -5) (-1 * 5glo + x * 5glo) + -1log[5](x + 4) = log[5](x + -5) (-5glo + 5glox) + -1log[5](x + 4) = log[5](x + -5) Reorder the terms: -5glo + 5glox + -1glo * 5(4 + x) = log[5](x + -5) Reorder the terms for easier multiplication: -5glo + 5glox + -1 * 5glo(4 + x) = log[5](x + -5) Multiply -1 * 5 -5glo + 5glox + -5glo(4 + x) = log[5](x + -5) -5glo + 5glox + (4 * -5glo + x * -5glo) = log[5](x + -5) -5glo + 5glox + (-20glo + -5glox) = log[5](x + -5) Reorder the terms: -5glo + -20glo + 5glox + -5glox = log[5](x + -5) Combine like terms: -5glo + -20glo = -25glo -25glo + 5glox + -5glox = log[5](x + -5) Combine like terms: 5glox + -5glox = 0 -25glo + 0 = log[5](x + -5) -25glo = log[5](x + -5) Reorder the terms: -25glo = glo * 5(-5 + x) Reorder the terms for easier multiplication: -25glo = 5glo(-5 + x) -25glo = (-5 * 5glo + x * 5glo) -25glo = (-25glo + 5glox) Add '25glo' to each side of the equation. -25glo + 25glo = -25glo + 25glo + 5glox Combine like terms: -25glo + 25glo = 0 0 = -25glo + 25glo + 5glox Combine like terms: -25glo + 25glo = 0 0 = 0 + 5glox 0 = 5glox Solving 0 = 5glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-5glox' to each side of the equation. 0 + -5glox = 5glox + -5glox Remove the zero: -5glox = 5glox + -5glox Combine like terms: 5glox + -5glox = 0 -5glox = 0 Divide each side by '-5'. glox = 0 Simplifying glox = 0 The solution to this equation could not be determined.
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