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Simplifying log(2x) = log(48 + -1x2) Remove parenthesis around (2x) glo * 2x = log(48 + -1x2) Reorder the terms for easier multiplication: 2glo * x = log(48 + -1x2) Multiply glo * x 2glox = log(48 + -1x2) 2glox = (48 * glo + -1x2 * glo) 2glox = (48glo + -1glox2) Solving 2glox = 48glo + -1glox2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-48glo' to each side of the equation. -48glo + 2glox = 48glo + -48glo + -1glox2 Combine like terms: 48glo + -48glo = 0 -48glo + 2glox = 0 + -1glox2 -48glo + 2glox = -1glox2 Add 'glox2' to each side of the equation. -48glo + 2glox + glox2 = -1glox2 + glox2 Combine like terms: -1glox2 + glox2 = 0 -48glo + 2glox + glox2 = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-48 + 2x + x2) = 0 Factor a trinomial. glo((-8 + -1x)(6 + -1x)) = 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 '(-8 + -1x)' equal to zero and attempt to solve: Simplifying -8 + -1x = 0 Solving -8 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1x = 0 + 8 -1x = 0 + 8 Combine like terms: 0 + 8 = 8 -1x = 8 Add 'x' to each side of the equation. -1x + x = 8 + x Combine like terms: -1x + x = 0 0 = 8 + x Simplifying 0 = 8 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Add 'x' to each side of the equation. -1x + x = -6 + x Combine like terms: -1x + x = 0 0 = -6 + x Simplifying 0 = -6 + 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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