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Simplifying Log[5](x + 7) = 1 + -1log[5](x + 3) Reorder the terms: goL * 5(7 + x) = 1 + -1log[5](x + 3) Reorder the terms for easier multiplication: 5goL(7 + x) = 1 + -1log[5](x + 3) (7 * 5goL + x * 5goL) = 1 + -1log[5](x + 3) (35goL + 5goxL) = 1 + -1log[5](x + 3) Reorder the terms: 35goL + 5goxL = 1 + -1glo * 5(3 + x) Reorder the terms for easier multiplication: 35goL + 5goxL = 1 + -1 * 5glo(3 + x) Multiply -1 * 5 35goL + 5goxL = 1 + -5glo(3 + x) 35goL + 5goxL = 1 + (3 * -5glo + x * -5glo) 35goL + 5goxL = 1 + (-15glo + -5glox) Solving 35goL + 5goxL = 1 + -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. 35goL + 15glo + 5goxL = 1 + -15glo + 15glo + -5glox Reorder the terms: 15glo + 35goL + 5goxL = 1 + -15glo + 15glo + -5glox Combine like terms: -15glo + 15glo = 0 15glo + 35goL + 5goxL = 1 + 0 + -5glox 15glo + 35goL + 5goxL = 1 + -5glox Add '5glox' to each side of the equation. 15glo + 35goL + 5glox + 5goxL = 1 + -5glox + 5glox Reorder the terms: 15glo + 5glox + 35goL + 5goxL = 1 + -5glox + 5glox Combine like terms: -5glox + 5glox = 0 15glo + 5glox + 35goL + 5goxL = 1 + 0 15glo + 5glox + 35goL + 5goxL = 1 Reorder the terms: -1 + 15glo + 5glox + 35goL + 5goxL = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 15glo + 5glox + 35goL + 5goxL = 0 The solution to this equation could not be determined.
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