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Simplifying log[2](3x) = log[2](5x + -10) Remove parenthesis around (3x) glo * 2 * 3x = log[2](5x + -10) Reorder the terms for easier multiplication: 2 * 3glo * x = log[2](5x + -10) Multiply 2 * 3 6glo * x = log[2](5x + -10) Multiply glo * x 6glox = log[2](5x + -10) Reorder the terms: 6glox = glo * 2(-10 + 5x) Reorder the terms for easier multiplication: 6glox = 2glo(-10 + 5x) 6glox = (-10 * 2glo + 5x * 2glo) 6glox = (-20glo + 10glox) Solving 6glox = -20glo + 10glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '20glo' to each side of the equation. 20glo + 6glox = -20glo + 20glo + 10glox Combine like terms: -20glo + 20glo = 0 20glo + 6glox = 0 + 10glox 20glo + 6glox = 10glox Add '-10glox' to each side of the equation. 20glo + 6glox + -10glox = 10glox + -10glox Combine like terms: 6glox + -10glox = -4glox 20glo + -4glox = 10glox + -10glox Combine like terms: 10glox + -10glox = 0 20glo + -4glox = 0 Factor out the Greatest Common Factor (GCF), '4glo'. 4glo(5 + -1x) = 0 Ignore the factor 4.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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Add 'x' to each side of the equation. -1x + x = -5 + x Combine like terms: -1x + x = 0 0 = -5 + x Simplifying 0 = -5 + x 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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