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Simplifying log[5](x + 2) + -1log[5] * x = log[5](x + 5) Reorder the terms: glo * 5(2 + x) + -1log[5] * x = log[5](x + 5) Reorder the terms for easier multiplication: 5glo(2 + x) + -1log[5] * x = log[5](x + 5) (2 * 5glo + x * 5glo) + -1log[5] * x = log[5](x + 5) (10glo + 5glox) + -1log[5] * x = log[5](x + 5) Reorder the terms for easier multiplication: 10glo + 5glox + -1 * 5glo * x = log[5](x + 5) Multiply -1 * 5 10glo + 5glox + -5glo * x = log[5](x + 5) Multiply glo * x 10glo + 5glox + -5glox = log[5](x + 5) Combine like terms: 5glox + -5glox = 0 10glo + 0 = log[5](x + 5) 10glo = log[5](x + 5) Reorder the terms: 10glo = glo * 5(5 + x) Reorder the terms for easier multiplication: 10glo = 5glo(5 + x) 10glo = (5 * 5glo + x * 5glo) 10glo = (25glo + 5glox) Solving 10glo = 25glo + 5glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-25glo' to each side of the equation. 10glo + -25glo = 25glo + -25glo + 5glox Combine like terms: 10glo + -25glo = -15glo -15glo = 25glo + -25glo + 5glox Combine like terms: 25glo + -25glo = 0 -15glo = 0 + 5glox -15glo = 5glox Add '-5glox' to each side of the equation. -15glo + -5glox = 5glox + -5glox Combine like terms: 5glox + -5glox = 0 -15glo + -5glox = 0 Factor out the Greatest Common Factor (GCF), '-5glo'. -5glo(3 + x) = 0 Ignore the factor -5.Subproblem 1
Set the factor 'glo' equal to zero and attempt to solve: Simplifying glo = 0 Solving glo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying glo = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Add '-1x' to each side of the equation. x + -1x = -3 + -1x Combine like terms: x + -1x = 0 0 = -3 + -1x Simplifying 0 = -3 + -1x 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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