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Simplifying log(x + 11) + -1log(2) = log(3x + 2) Reorder the terms: glo(11 + x) + -1log(2) = log(3x + 2) (11 * glo + x * glo) + -1log(2) = log(3x + 2) (11glo + glox) + -1log(2) = log(3x + 2) Reorder the terms for easier multiplication: 11glo + glox + -1 * 2glo = log(3x + 2) Multiply -1 * 2 11glo + glox + -2glo = log(3x + 2) Reorder the terms: 11glo + -2glo + glox = log(3x + 2) Combine like terms: 11glo + -2glo = 9glo 9glo + glox = log(3x + 2) Reorder the terms: 9glo + glox = glo(2 + 3x) 9glo + glox = (2 * glo + 3x * glo) 9glo + glox = (2glo + 3glox) Solving 9glo + glox = 2glo + 3glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-2glo' to each side of the equation. 9glo + -2glo + glox = 2glo + -2glo + 3glox Combine like terms: 9glo + -2glo = 7glo 7glo + glox = 2glo + -2glo + 3glox Combine like terms: 2glo + -2glo = 0 7glo + glox = 0 + 3glox 7glo + glox = 3glox Add '-3glox' to each side of the equation. 7glo + glox + -3glox = 3glox + -3glox Combine like terms: glox + -3glox = -2glox 7glo + -2glox = 3glox + -3glox Combine like terms: 3glox + -3glox = 0 7glo + -2glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(7 + -2x) = 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 '(7 + -2x)' equal to zero and attempt to solve: Simplifying 7 + -2x = 0 Solving 7 + -2x = 0 Move all terms containing g to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2x = 0 + -7 -2x = 0 + -7 Combine like terms: 0 + -7 = -7 -2x = -7 Add '2x' to each side of the equation. -2x + 2x = -7 + 2x Combine like terms: -2x + 2x = 0 0 = -7 + 2x Simplifying 0 = -7 + 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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