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Simplifying log[5](x + 1) = 4 + log[5](x + -5) Reorder the terms: glo * 5(1 + x) = 4 + log[5](x + -5) Reorder the terms for easier multiplication: 5glo(1 + x) = 4 + log[5](x + -5) (1 * 5glo + x * 5glo) = 4 + log[5](x + -5) (5glo + 5glox) = 4 + log[5](x + -5) Reorder the terms: 5glo + 5glox = 4 + glo * 5(-5 + x) Reorder the terms for easier multiplication: 5glo + 5glox = 4 + 5glo(-5 + x) 5glo + 5glox = 4 + (-5 * 5glo + x * 5glo) 5glo + 5glox = 4 + (-25glo + 5glox) Add '-5glox' to each side of the equation. 5glo + 5glox + -5glox = 4 + -25glo + 5glox + -5glox Combine like terms: 5glox + -5glox = 0 5glo + 0 = 4 + -25glo + 5glox + -5glox 5glo = 4 + -25glo + 5glox + -5glox Combine like terms: 5glox + -5glox = 0 5glo = 4 + -25glo + 0 5glo = 4 + -25glo Solving 5glo = 4 + -25glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '25glo' to each side of the equation. 5glo + 25glo = 4 + -25glo + 25glo Combine like terms: 5glo + 25glo = 30glo 30glo = 4 + -25glo + 25glo Combine like terms: -25glo + 25glo = 0 30glo = 4 + 0 30glo = 4 Divide each side by '30lo'. g = 0.1333333333l-1o-1 Simplifying g = 0.1333333333l-1o-1
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