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Simplifying log(6x + -2) = log(8x + -10) Reorder the terms: glo(-2 + 6x) = log(8x + -10) (-2 * glo + 6x * glo) = log(8x + -10) (-2glo + 6glox) = log(8x + -10) Reorder the terms: -2glo + 6glox = glo(-10 + 8x) -2glo + 6glox = (-10 * glo + 8x * glo) -2glo + 6glox = (-10glo + 8glox) Solving -2glo + 6glox = -10glo + 8glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '10glo' to each side of the equation. -2glo + 10glo + 6glox = -10glo + 10glo + 8glox Combine like terms: -2glo + 10glo = 8glo 8glo + 6glox = -10glo + 10glo + 8glox Combine like terms: -10glo + 10glo = 0 8glo + 6glox = 0 + 8glox 8glo + 6glox = 8glox Add '-8glox' to each side of the equation. 8glo + 6glox + -8glox = 8glox + -8glox Combine like terms: 6glox + -8glox = -2glox 8glo + -2glox = 8glox + -8glox Combine like terms: 8glox + -8glox = 0 8glo + -2glox = 0 Factor out the Greatest Common Factor (GCF), '2glo'. 2glo(4 + -1x) = 0 Ignore the factor 2.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 '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Add 'x' to each side of the equation. -1x + x = -4 + x Combine like terms: -1x + x = 0 0 = -4 + x Simplifying 0 = -4 + x 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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