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Simplifying log(3x + -10) = 2 + log(x + -2) Reorder the terms: glo(-10 + 3x) = 2 + log(x + -2) (-10 * glo + 3x * glo) = 2 + log(x + -2) (-10glo + 3glox) = 2 + log(x + -2) Reorder the terms: -10glo + 3glox = 2 + glo(-2 + x) -10glo + 3glox = 2 + (-2 * glo + x * glo) -10glo + 3glox = 2 + (-2glo + glox) Solving -10glo + 3glox = 2 + -2glo + glox 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. -10glo + 2glo + 3glox = 2 + -2glo + 2glo + glox Combine like terms: -10glo + 2glo = -8glo -8glo + 3glox = 2 + -2glo + 2glo + glox Combine like terms: -2glo + 2glo = 0 -8glo + 3glox = 2 + 0 + glox -8glo + 3glox = 2 + glox Add '-1glox' to each side of the equation. -8glo + 3glox + -1glox = 2 + glox + -1glox Combine like terms: 3glox + -1glox = 2glox -8glo + 2glox = 2 + glox + -1glox Combine like terms: glox + -1glox = 0 -8glo + 2glox = 2 + 0 -8glo + 2glox = 2 Reorder the terms: -2 + -8glo + 2glox = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -8glo + 2glox = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -4glo + glox) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -4glo + glox)' equal to zero and attempt to solve: Simplifying -1 + -4glo + glox = 0 Solving -1 + -4glo + glox = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + -4glo + 1 + glox = 0 + 1 Reorder the terms: -1 + 1 + -4glo + glox = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4glo + glox = 0 + 1 -4glo + glox = 0 + 1 Combine like terms: 0 + 1 = 1 -4glo + glox = 1 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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