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Simplifying log[5](28 + 3x) + -1log[5](x) = log[5](x + 6) Reorder the terms for easier multiplication: 5glo(28 + 3x) + -1log[5](x) = log[5](x + 6) (28 * 5glo + 3x * 5glo) + -1log[5](x) = log[5](x + 6) (140glo + 15glox) + -1log[5](x) = log[5](x + 6) Reorder the terms for easier multiplication: 140glo + 15glox + -1 * 5glo * x = log[5](x + 6) Multiply -1 * 5 140glo + 15glox + -5glo * x = log[5](x + 6) Multiply glo * x 140glo + 15glox + -5glox = log[5](x + 6) Combine like terms: 15glox + -5glox = 10glox 140glo + 10glox = log[5](x + 6) Reorder the terms: 140glo + 10glox = glo * 5(6 + x) Reorder the terms for easier multiplication: 140glo + 10glox = 5glo(6 + x) 140glo + 10glox = (6 * 5glo + x * 5glo) 140glo + 10glox = (30glo + 5glox) Solving 140glo + 10glox = 30glo + 5glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-30glo' to each side of the equation. 140glo + -30glo + 10glox = 30glo + -30glo + 5glox Combine like terms: 140glo + -30glo = 110glo 110glo + 10glox = 30glo + -30glo + 5glox Combine like terms: 30glo + -30glo = 0 110glo + 10glox = 0 + 5glox 110glo + 10glox = 5glox Add '-5glox' to each side of the equation. 110glo + 10glox + -5glox = 5glox + -5glox Combine like terms: 10glox + -5glox = 5glox 110glo + 5glox = 5glox + -5glox Combine like terms: 5glox + -5glox = 0 110glo + 5glox = 0 Factor out the Greatest Common Factor (GCF), '5glo'. 5glo(22 + 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 '(22 + x)' equal to zero and attempt to solve: Simplifying 22 + x = 0 Solving 22 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + x = 0 + -22 Combine like terms: 22 + -22 = 0 0 + x = 0 + -22 x = 0 + -22 Combine like terms: 0 + -22 = -22 x = -22 Add '-1x' to each side of the equation. x + -1x = -22 + -1x Combine like terms: x + -1x = 0 0 = -22 + -1x Simplifying 0 = -22 + -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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