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Simplifying 2log(x) = log(2) + log(4x + 10) Multiply glo * x 2glox = log(2) + log(4x + 10) Reorder the terms for easier multiplication: 2glox = 2glo + log(4x + 10) Reorder the terms: 2glox = 2glo + glo(10 + 4x) 2glox = 2glo + (10 * glo + 4x * glo) 2glox = 2glo + (10glo + 4glox) Combine like terms: 2glo + 10glo = 12glo 2glox = 12glo + 4glox Solving 2glox = 12glo + 4glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-12glo' to each side of the equation. -12glo + 2glox = 12glo + -12glo + 4glox Combine like terms: 12glo + -12glo = 0 -12glo + 2glox = 0 + 4glox -12glo + 2glox = 4glox Add '-4glox' to each side of the equation. -12glo + 2glox + -4glox = 4glox + -4glox Combine like terms: 2glox + -4glox = -2glox -12glo + -2glox = 4glox + -4glox Combine like terms: 4glox + -4glox = 0 -12glo + -2glox = 0 Factor out the Greatest Common Factor (GCF), '-2glo'. -2glo(6 + x) = 0 Ignore the factor -2.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 '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 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 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Add '-1x' to each side of the equation. x + -1x = -6 + -1x Combine like terms: x + -1x = 0 0 = -6 + -1x Simplifying 0 = -6 + -1x 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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