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Simplifying log[3](x + 1) + log[3](x + 7) = 3 Reorder the terms: glo * 3(1 + x) + log[3](x + 7) = 3 Reorder the terms for easier multiplication: 3glo(1 + x) + log[3](x + 7) = 3 (1 * 3glo + x * 3glo) + log[3](x + 7) = 3 (3glo + 3glox) + log[3](x + 7) = 3 Reorder the terms: 3glo + 3glox + glo * 3(7 + x) = 3 Reorder the terms for easier multiplication: 3glo + 3glox + 3glo(7 + x) = 3 3glo + 3glox + (7 * 3glo + x * 3glo) = 3 3glo + 3glox + (21glo + 3glox) = 3 Reorder the terms: 3glo + 21glo + 3glox + 3glox = 3 Combine like terms: 3glo + 21glo = 24glo 24glo + 3glox + 3glox = 3 Combine like terms: 3glox + 3glox = 6glox 24glo + 6glox = 3 Solving 24glo + 6glox = 3 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Reorder the terms: -3 + 24glo + 6glox = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 24glo + 6glox = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + 8glo + 2glox) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + 8glo + 2glox)' equal to zero and attempt to solve: Simplifying -1 + 8glo + 2glox = 0 Solving -1 + 8glo + 2glox = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 8glo + 1 + 2glox = 0 + 1 Reorder the terms: -1 + 1 + 8glo + 2glox = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 8glo + 2glox = 0 + 1 8glo + 2glox = 0 + 1 Combine like terms: 0 + 1 = 1 8glo + 2glox = 1 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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