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Simplifying log[5](x + 17) = 3 + -1log[5](x + -3) Reorder the terms: glo * 5(17 + x) = 3 + -1log[5](x + -3) Reorder the terms for easier multiplication: 5glo(17 + x) = 3 + -1log[5](x + -3) (17 * 5glo + x * 5glo) = 3 + -1log[5](x + -3) (85glo + 5glox) = 3 + -1log[5](x + -3) Reorder the terms: 85glo + 5glox = 3 + -1glo * 5(-3 + x) Reorder the terms for easier multiplication: 85glo + 5glox = 3 + -1 * 5glo(-3 + x) Multiply -1 * 5 85glo + 5glox = 3 + -5glo(-3 + x) 85glo + 5glox = 3 + (-3 * -5glo + x * -5glo) 85glo + 5glox = 3 + (15glo + -5glox) Solving 85glo + 5glox = 3 + 15glo + -5glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-15glo' to each side of the equation. 85glo + -15glo + 5glox = 3 + 15glo + -15glo + -5glox Combine like terms: 85glo + -15glo = 70glo 70glo + 5glox = 3 + 15glo + -15glo + -5glox Combine like terms: 15glo + -15glo = 0 70glo + 5glox = 3 + 0 + -5glox 70glo + 5glox = 3 + -5glox Add '5glox' to each side of the equation. 70glo + 5glox + 5glox = 3 + -5glox + 5glox Combine like terms: 5glox + 5glox = 10glox 70glo + 10glox = 3 + -5glox + 5glox Combine like terms: -5glox + 5glox = 0 70glo + 10glox = 3 + 0 70glo + 10glox = 3 Reorder the terms: -3 + 70glo + 10glox = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 70glo + 10glox = 0 The solution to this equation could not be determined.
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