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Simplifying log[2](9x + -10) + log[2](x + 8) = 2log[2](3x) Reorder the terms: glo * 2(-10 + 9x) + log[2](x + 8) = 2log[2](3x) Reorder the terms for easier multiplication: 2glo(-10 + 9x) + log[2](x + 8) = 2log[2](3x) (-10 * 2glo + 9x * 2glo) + log[2](x + 8) = 2log[2](3x) (-20glo + 18glox) + log[2](x + 8) = 2log[2](3x) Reorder the terms: -20glo + 18glox + glo * 2(8 + x) = 2log[2](3x) Reorder the terms for easier multiplication: -20glo + 18glox + 2glo(8 + x) = 2log[2](3x) -20glo + 18glox + (8 * 2glo + x * 2glo) = 2log[2](3x) -20glo + 18glox + (16glo + 2glox) = 2log[2](3x) Reorder the terms: -20glo + 16glo + 18glox + 2glox = 2log[2](3x) Combine like terms: -20glo + 16glo = -4glo -4glo + 18glox + 2glox = 2log[2](3x) Combine like terms: 18glox + 2glox = 20glox -4glo + 20glox = 2log[2](3x) Remove parenthesis around (3x) -4glo + 20glox = 2glo * 2 * 3x Reorder the terms for easier multiplication: -4glo + 20glox = 2 * 2 * 3glo * x Multiply 2 * 2 -4glo + 20glox = 4 * 3glo * x Multiply 4 * 3 -4glo + 20glox = 12glo * x Multiply glo * x -4glo + 20glox = 12glox Solving -4glo + 20glox = 12glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-12glox' to each side of the equation. -4glo + 20glox + -12glox = 12glox + -12glox Combine like terms: 20glox + -12glox = 8glox -4glo + 8glox = 12glox + -12glox Combine like terms: 12glox + -12glox = 0 -4glo + 8glox = 0 Factor out the Greatest Common Factor (GCF), '4glo'. 4glo(-1 + 2x) = 0 Ignore the factor 4.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 + 2x)' equal to zero and attempt to solve: Simplifying -1 + 2x = 0 Solving -1 + 2x = 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 + 2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2x = 0 + 1 2x = 0 + 1 Combine like terms: 0 + 1 = 1 2x = 1 Add '-2x' to each side of the equation. 2x + -2x = 1 + -2x Combine like terms: 2x + -2x = 0 0 = 1 + -2x Simplifying 0 = 1 + -2x 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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