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Simplifying log(51x) + log(2x) = log(3x) + log(1) Remove parenthesis around (51x) glo * 51x + log(2x) = log(3x) + log(1) Reorder the terms for easier multiplication: 51glo * x + log(2x) = log(3x) + log(1) Multiply glo * x 51glox + log(2x) = log(3x) + log(1) Remove parenthesis around (2x) 51glox + glo * 2x = log(3x) + log(1) Reorder the terms for easier multiplication: 51glox + 2glo * x = log(3x) + log(1) Multiply glo * x 51glox + 2glox = log(3x) + log(1) Combine like terms: 51glox + 2glox = 53glox 53glox = log(3x) + log(1) Remove parenthesis around (3x) 53glox = glo * 3x + log(1) Reorder the terms for easier multiplication: 53glox = 3glo * x + log(1) Multiply glo * x 53glox = 3glox + log(1) Reorder the terms for easier multiplication: 53glox = 3glox + 1glo Reorder the terms: 53glox = 1glo + 3glox Solving 53glox = 1glo + 3glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-1glo' to each side of the equation. -1glo + 53glox = 1glo + -1glo + 3glox Combine like terms: 1glo + -1glo = 0 -1glo + 53glox = 0 + 3glox -1glo + 53glox = 3glox Add '-3glox' to each side of the equation. -1glo + 53glox + -3glox = 3glox + -3glox Combine like terms: 53glox + -3glox = 50glox -1glo + 50glox = 3glox + -3glox Combine like terms: 3glox + -3glox = 0 -1glo + 50glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-1 + 50x) = 0Subproblem 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 + 50x)' equal to zero and attempt to solve: Simplifying -1 + 50x = 0 Solving -1 + 50x = 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 + 50x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 50x = 0 + 1 50x = 0 + 1 Combine like terms: 0 + 1 = 1 50x = 1 Add '-50x' to each side of the equation. 50x + -50x = 1 + -50x Combine like terms: 50x + -50x = 0 0 = 1 + -50x Simplifying 0 = 1 + -50x 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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