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Simplifying log[2](3x + 2) = log[3](12x + 3) Reorder the terms: glo * 2(2 + 3x) = log[3](12x + 3) Reorder the terms for easier multiplication: 2glo(2 + 3x) = log[3](12x + 3) (2 * 2glo + 3x * 2glo) = log[3](12x + 3) (4glo + 6glox) = log[3](12x + 3) Reorder the terms: 4glo + 6glox = glo * 3(3 + 12x) Reorder the terms for easier multiplication: 4glo + 6glox = 3glo(3 + 12x) 4glo + 6glox = (3 * 3glo + 12x * 3glo) 4glo + 6glox = (9glo + 36glox) Solving 4glo + 6glox = 9glo + 36glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-9glo' to each side of the equation. 4glo + -9glo + 6glox = 9glo + -9glo + 36glox Combine like terms: 4glo + -9glo = -5glo -5glo + 6glox = 9glo + -9glo + 36glox Combine like terms: 9glo + -9glo = 0 -5glo + 6glox = 0 + 36glox -5glo + 6glox = 36glox Add '-36glox' to each side of the equation. -5glo + 6glox + -36glox = 36glox + -36glox Combine like terms: 6glox + -36glox = -30glox -5glo + -30glox = 36glox + -36glox Combine like terms: 36glox + -36glox = 0 -5glo + -30glox = 0 Factor out the Greatest Common Factor (GCF), '-5glo'. -5glo(1 + 6x) = 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 + 6x)' equal to zero and attempt to solve: Simplifying 1 + 6x = 0 Solving 1 + 6x = 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 + 6x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6x = 0 + -1 6x = 0 + -1 Combine like terms: 0 + -1 = -1 6x = -1 Add '-6x' to each side of the equation. 6x + -6x = -1 + -6x Combine like terms: 6x + -6x = 0 0 = -1 + -6x Simplifying 0 = -1 + -6x 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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