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Simplifying log(4x + -13) + log(x + 10) = 2log(2x) Reorder the terms: glo(-13 + 4x) + log(x + 10) = 2log(2x) (-13 * glo + 4x * glo) + log(x + 10) = 2log(2x) (-13glo + 4glox) + log(x + 10) = 2log(2x) Reorder the terms: -13glo + 4glox + glo(10 + x) = 2log(2x) -13glo + 4glox + (10 * glo + x * glo) = 2log(2x) -13glo + 4glox + (10glo + glox) = 2log(2x) Reorder the terms: -13glo + 10glo + 4glox + glox = 2log(2x) Combine like terms: -13glo + 10glo = -3glo -3glo + 4glox + glox = 2log(2x) Combine like terms: 4glox + glox = 5glox -3glo + 5glox = 2log(2x) Remove parenthesis around (2x) -3glo + 5glox = 2glo * 2x Reorder the terms for easier multiplication: -3glo + 5glox = 2 * 2glo * x Multiply 2 * 2 -3glo + 5glox = 4glo * x Multiply glo * x -3glo + 5glox = 4glox Solving -3glo + 5glox = 4glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-4glox' to each side of the equation. -3glo + 5glox + -4glox = 4glox + -4glox Combine like terms: 5glox + -4glox = 1glox -3glo + 1glox = 4glox + -4glox Combine like terms: 4glox + -4glox = 0 -3glo + 1glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-3 + x) = 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 '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Add '-1x' to each side of the equation. x + -1x = 3 + -1x Combine like terms: x + -1x = 0 0 = 3 + -1x Simplifying 0 = 3 + -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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