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