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Simplifying log[5](2) + 2log[5](x) = log[5](3 + -1x) Reorder the terms for easier multiplication: 5 * 2glo + 2log[5](x) = log[5](3 + -1x) Multiply 5 * 2 10glo + 2log[5](x) = log[5](3 + -1x) Reorder the terms for easier multiplication: 10glo + 2 * 5glo * x = log[5](3 + -1x) Multiply 2 * 5 10glo + 10glo * x = log[5](3 + -1x) Multiply glo * x 10glo + 10glox = log[5](3 + -1x) Reorder the terms for easier multiplication: 10glo + 10glox = 5glo(3 + -1x) 10glo + 10glox = (3 * 5glo + -1x * 5glo) 10glo + 10glox = (15glo + -5glox) Solving 10glo + 10glox = 15glo + -5glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-15glo' to each side of the equation. 10glo + -15glo + 10glox = 15glo + -15glo + -5glox Combine like terms: 10glo + -15glo = -5glo -5glo + 10glox = 15glo + -15glo + -5glox Combine like terms: 15glo + -15glo = 0 -5glo + 10glox = 0 + -5glox -5glo + 10glox = -5glox Add '5glox' to each side of the equation. -5glo + 10glox + 5glox = -5glox + 5glox Combine like terms: 10glox + 5glox = 15glox -5glo + 15glox = -5glox + 5glox Combine like terms: -5glox + 5glox = 0 -5glo + 15glox = 0 Factor out the Greatest Common Factor (GCF), '5glo'. 5glo(-1 + 3x) = 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 '(-1 + 3x)' equal to zero and attempt to solve: Simplifying -1 + 3x = 0 Solving -1 + 3x = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 3x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 3x = 0 + 1 3x = 0 + 1 Combine like terms: 0 + 1 = 1 3x = 1 Add '-3x' to each side of the equation. 3x + -3x = 1 + -3x Combine like terms: 3x + -3x = 0 0 = 1 + -3x Simplifying 0 = 1 + -3x 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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