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Simplifying log(6x + -2) + -1log(2x + -1) = log(7) Reorder the terms: glo(-2 + 6x) + -1log(2x + -1) = log(7) (-2 * glo + 6x * glo) + -1log(2x + -1) = log(7) (-2glo + 6glox) + -1log(2x + -1) = log(7) Reorder the terms: -2glo + 6glox + -1glo(-1 + 2x) = log(7) -2glo + 6glox + (-1 * -1glo + 2x * -1glo) = log(7) -2glo + 6glox + (1glo + -2glox) = log(7) Reorder the terms: -2glo + 1glo + 6glox + -2glox = log(7) Combine like terms: -2glo + 1glo = -1glo -1glo + 6glox + -2glox = log(7) Combine like terms: 6glox + -2glox = 4glox -1glo + 4glox = log(7) Reorder the terms for easier multiplication: -1glo + 4glox = 7glo Solving -1glo + 4glox = 7glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-7glo' to each side of the equation. -1glo + -7glo + 4glox = 7glo + -7glo Combine like terms: -1glo + -7glo = -8glo -8glo + 4glox = 7glo + -7glo Combine like terms: 7glo + -7glo = 0 -8glo + 4glox = 0 Factor out the Greatest Common Factor (GCF), '4glo'. 4glo(-2 + x) = 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 '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Add '-1x' to each side of the equation. x + -1x = 2 + -1x Combine like terms: x + -1x = 0 0 = 2 + -1x Simplifying 0 = 2 + -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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