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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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