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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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