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Simplifying log(3x + -2) = log(2x + 5) Reorder the terms: glo(-2 + 3x) = log(2x + 5) (-2 * glo + 3x * glo) = log(2x + 5) (-2glo + 3glox) = log(2x + 5) Reorder the terms: -2glo + 3glox = glo(5 + 2x) -2glo + 3glox = (5 * glo + 2x * glo) -2glo + 3glox = (5glo + 2glox) Solving -2glo + 3glox = 5glo + 2glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-5glo' to each side of the equation. -2glo + -5glo + 3glox = 5glo + -5glo + 2glox Combine like terms: -2glo + -5glo = -7glo -7glo + 3glox = 5glo + -5glo + 2glox Combine like terms: 5glo + -5glo = 0 -7glo + 3glox = 0 + 2glox -7glo + 3glox = 2glox Add '-2glox' to each side of the equation. -7glo + 3glox + -2glox = 2glox + -2glox Combine like terms: 3glox + -2glox = 1glox -7glo + 1glox = 2glox + -2glox Combine like terms: 2glox + -2glox = 0 -7glo + 1glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-7 + x) = 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 + x)' equal to zero and attempt to solve: Simplifying -7 + x = 0 Solving -7 + x = 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 + x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + x = 0 + 7 x = 0 + 7 Combine like terms: 0 + 7 = 7 x = 7 Add '-1x' to each side of the equation. x + -1x = 7 + -1x Combine like terms: x + -1x = 0 0 = 7 + -1x Simplifying 0 = 7 + -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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