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Simplifying log(4x + -2) = log(5 + -5x) Reorder the terms: glo(-2 + 4x) = log(5 + -5x) (-2 * glo + 4x * glo) = log(5 + -5x) (-2glo + 4glox) = log(5 + -5x) -2glo + 4glox = (5 * glo + -5x * glo) -2glo + 4glox = (5glo + -5glox) Solving -2glo + 4glox = 5glo + -5glox 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 + 4glox = 5glo + -5glo + -5glox Combine like terms: -2glo + -5glo = -7glo -7glo + 4glox = 5glo + -5glo + -5glox Combine like terms: 5glo + -5glo = 0 -7glo + 4glox = 0 + -5glox -7glo + 4glox = -5glox Add '5glox' to each side of the equation. -7glo + 4glox + 5glox = -5glox + 5glox Combine like terms: 4glox + 5glox = 9glox -7glo + 9glox = -5glox + 5glox Combine like terms: -5glox + 5glox = 0 -7glo + 9glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-7 + 9x) = 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 + 9x)' equal to zero and attempt to solve: Simplifying -7 + 9x = 0 Solving -7 + 9x = 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 + 9x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 9x = 0 + 7 9x = 0 + 7 Combine like terms: 0 + 7 = 7 9x = 7 Add '-9x' to each side of the equation. 9x + -9x = 7 + -9x Combine like terms: 9x + -9x = 0 0 = 7 + -9x Simplifying 0 = 7 + -9x 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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