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Simplifying log(-5x) = log(4x + -9) Remove parenthesis around (-5x) glo * -5x = log(4x + -9) Reorder the terms for easier multiplication: -5glo * x = log(4x + -9) Multiply glo * x -5glox = log(4x + -9) Reorder the terms: -5glox = glo(-9 + 4x) -5glox = (-9 * glo + 4x * glo) -5glox = (-9glo + 4glox) Solving -5glox = -9glo + 4glox 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. 9glo + -5glox = -9glo + 9glo + 4glox Combine like terms: -9glo + 9glo = 0 9glo + -5glox = 0 + 4glox 9glo + -5glox = 4glox Add '-4glox' to each side of the equation. 9glo + -5glox + -4glox = 4glox + -4glox Combine like terms: -5glox + -4glox = -9glox 9glo + -9glox = 4glox + -4glox Combine like terms: 4glox + -4glox = 0 9glo + -9glox = 0 Factor out the Greatest Common Factor (GCF), '9glo'. 9glo(1 + -1x) = 0 Ignore the factor 9.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 '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Add 'x' to each side of the equation. -1x + x = -1 + x Combine like terms: -1x + x = 0 0 = -1 + x Simplifying 0 = -1 + 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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