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Simplifying log[5](x + 6) + log[5](x + 30) = 2 Reorder the terms: glo * 5(6 + x) + log[5](x + 30) = 2 Reorder the terms for easier multiplication: 5glo(6 + x) + log[5](x + 30) = 2 (6 * 5glo + x * 5glo) + log[5](x + 30) = 2 (30glo + 5glox) + log[5](x + 30) = 2 Reorder the terms: 30glo + 5glox + glo * 5(30 + x) = 2 Reorder the terms for easier multiplication: 30glo + 5glox + 5glo(30 + x) = 2 30glo + 5glox + (30 * 5glo + x * 5glo) = 2 30glo + 5glox + (150glo + 5glox) = 2 Reorder the terms: 30glo + 150glo + 5glox + 5glox = 2 Combine like terms: 30glo + 150glo = 180glo 180glo + 5glox + 5glox = 2 Combine like terms: 5glox + 5glox = 10glox 180glo + 10glox = 2 Solving 180glo + 10glox = 2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Reorder the terms: -2 + 180glo + 10glox = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 180glo + 10glox = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 90glo + 5glox) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 90glo + 5glox)' equal to zero and attempt to solve: Simplifying -1 + 90glo + 5glox = 0 Solving -1 + 90glo + 5glox = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 90glo + 1 + 5glox = 0 + 1 Reorder the terms: -1 + 1 + 90glo + 5glox = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 90glo + 5glox = 0 + 1 90glo + 5glox = 0 + 1 Combine like terms: 0 + 1 = 1 90glo + 5glox = 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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