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Simplifying 2log[5](x + 2) = log[5](x + 8) Reorder the terms: 2glo * 5(2 + x) = log[5](x + 8) Reorder the terms for easier multiplication: 2 * 5glo(2 + x) = log[5](x + 8) Multiply 2 * 5 10glo(2 + x) = log[5](x + 8) (2 * 10glo + x * 10glo) = log[5](x + 8) (20glo + 10glox) = log[5](x + 8) Reorder the terms: 20glo + 10glox = glo * 5(8 + x) Reorder the terms for easier multiplication: 20glo + 10glox = 5glo(8 + x) 20glo + 10glox = (8 * 5glo + x * 5glo) 20glo + 10glox = (40glo + 5glox) Solving 20glo + 10glox = 40glo + 5glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-40glo' to each side of the equation. 20glo + -40glo + 10glox = 40glo + -40glo + 5glox Combine like terms: 20glo + -40glo = -20glo -20glo + 10glox = 40glo + -40glo + 5glox Combine like terms: 40glo + -40glo = 0 -20glo + 10glox = 0 + 5glox -20glo + 10glox = 5glox Add '-5glox' to each side of the equation. -20glo + 10glox + -5glox = 5glox + -5glox Combine like terms: 10glox + -5glox = 5glox -20glo + 5glox = 5glox + -5glox Combine like terms: 5glox + -5glox = 0 -20glo + 5glox = 0 Factor out the Greatest Common Factor (GCF), '5glo'. 5glo(-4 + 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 '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Add '-1x' to each side of the equation. x + -1x = 4 + -1x Combine like terms: x + -1x = 0 0 = 4 + -1x Simplifying 0 = 4 + -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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