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