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Simplifying log[5](x + 117) + log[5](x + -3) = 4 Reorder the terms: glo * 5(117 + x) + log[5](x + -3) = 4 Reorder the terms for easier multiplication: 5glo(117 + x) + log[5](x + -3) = 4 (117 * 5glo + x * 5glo) + log[5](x + -3) = 4 (585glo + 5glox) + log[5](x + -3) = 4 Reorder the terms: 585glo + 5glox + glo * 5(-3 + x) = 4 Reorder the terms for easier multiplication: 585glo + 5glox + 5glo(-3 + x) = 4 585glo + 5glox + (-3 * 5glo + x * 5glo) = 4 585glo + 5glox + (-15glo + 5glox) = 4 Reorder the terms: 585glo + -15glo + 5glox + 5glox = 4 Combine like terms: 585glo + -15glo = 570glo 570glo + 5glox + 5glox = 4 Combine like terms: 5glox + 5glox = 10glox 570glo + 10glox = 4 Solving 570glo + 10glox = 4 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Reorder the terms: -4 + 570glo + 10glox = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 570glo + 10glox = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 285glo + 5glox) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + 285glo + 5glox)' equal to zero and attempt to solve: Simplifying -2 + 285glo + 5glox = 0 Solving -2 + 285glo + 5glox = 0 Move all terms containing g to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 285glo + 2 + 5glox = 0 + 2 Reorder the terms: -2 + 2 + 285glo + 5glox = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 285glo + 5glox = 0 + 2 285glo + 5glox = 0 + 2 Combine like terms: 0 + 2 = 2 285glo + 5glox = 2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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