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Simplifying log[5](x + 8) = 1 + -1log[5](x + 4) Reorder the terms: glo * 5(8 + x) = 1 + -1log[5](x + 4) Reorder the terms for easier multiplication: 5glo(8 + x) = 1 + -1log[5](x + 4) (8 * 5glo + x * 5glo) = 1 + -1log[5](x + 4) (40glo + 5glox) = 1 + -1log[5](x + 4) Reorder the terms: 40glo + 5glox = 1 + -1glo * 5(4 + x) Reorder the terms for easier multiplication: 40glo + 5glox = 1 + -1 * 5glo(4 + x) Multiply -1 * 5 40glo + 5glox = 1 + -5glo(4 + x) 40glo + 5glox = 1 + (4 * -5glo + x * -5glo) 40glo + 5glox = 1 + (-20glo + -5glox) Solving 40glo + 5glox = 1 + -20glo + -5glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '20glo' to each side of the equation. 40glo + 20glo + 5glox = 1 + -20glo + 20glo + -5glox Combine like terms: 40glo + 20glo = 60glo 60glo + 5glox = 1 + -20glo + 20glo + -5glox Combine like terms: -20glo + 20glo = 0 60glo + 5glox = 1 + 0 + -5glox 60glo + 5glox = 1 + -5glox Add '5glox' to each side of the equation. 60glo + 5glox + 5glox = 1 + -5glox + 5glox Combine like terms: 5glox + 5glox = 10glox 60glo + 10glox = 1 + -5glox + 5glox Combine like terms: -5glox + 5glox = 0 60glo + 10glox = 1 + 0 60glo + 10glox = 1 Reorder the terms: -1 + 60glo + 10glox = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 60glo + 10glox = 0 The solution to this equation could not be determined.
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