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Simplifying 2log[5] * x = log[5] * 4 + log[5](3x + -1) Reorder the terms for easier multiplication: 2 * 5glo * x = log[5] * 4 + log[5](3x + -1) Multiply 2 * 5 10glo * x = log[5] * 4 + log[5](3x + -1) Multiply glo * x 10glox = log[5] * 4 + log[5](3x + -1) Reorder the terms for easier multiplication: 10glox = 5 * 4glo + log[5](3x + -1) Multiply 5 * 4 10glox = 20glo + log[5](3x + -1) Reorder the terms: 10glox = 20glo + glo * 5(-1 + 3x) Reorder the terms for easier multiplication: 10glox = 20glo + 5glo(-1 + 3x) 10glox = 20glo + (-1 * 5glo + 3x * 5glo) 10glox = 20glo + (-5glo + 15glox) Combine like terms: 20glo + -5glo = 15glo 10glox = 15glo + 15glox Solving 10glox = 15glo + 15glox 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. -15glo + 10glox = 15glo + -15glo + 15glox Combine like terms: 15glo + -15glo = 0 -15glo + 10glox = 0 + 15glox -15glo + 10glox = 15glox Add '-15glox' to each side of the equation. -15glo + 10glox + -15glox = 15glox + -15glox Combine like terms: 10glox + -15glox = -5glox -15glo + -5glox = 15glox + -15glox Combine like terms: 15glox + -15glox = 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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