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