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Simplifying log(5x + -5) = log(2x + 3) + log(15) Reorder the terms: glo(-5 + 5x) = log(2x + 3) + log(15) (-5 * glo + 5x * glo) = log(2x + 3) + log(15) (-5glo + 5glox) = log(2x + 3) + log(15) Reorder the terms: -5glo + 5glox = glo(3 + 2x) + log(15) -5glo + 5glox = (3 * glo + 2x * glo) + log(15) -5glo + 5glox = (3glo + 2glox) + log(15) Reorder the terms for easier multiplication: -5glo + 5glox = 3glo + 2glox + 15glo Reorder the terms: -5glo + 5glox = 3glo + 15glo + 2glox Combine like terms: 3glo + 15glo = 18glo -5glo + 5glox = 18glo + 2glox Solving -5glo + 5glox = 18glo + 2glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-18glo' to each side of the equation. -5glo + -18glo + 5glox = 18glo + -18glo + 2glox Combine like terms: -5glo + -18glo = -23glo -23glo + 5glox = 18glo + -18glo + 2glox Combine like terms: 18glo + -18glo = 0 -23glo + 5glox = 0 + 2glox -23glo + 5glox = 2glox Add '-2glox' to each side of the equation. -23glo + 5glox + -2glox = 2glox + -2glox Combine like terms: 5glox + -2glox = 3glox -23glo + 3glox = 2glox + -2glox Combine like terms: 2glox + -2glox = 0 -23glo + 3glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-23 + 3x) = 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 '(-23 + 3x)' equal to zero and attempt to solve: Simplifying -23 + 3x = 0 Solving -23 + 3x = 0 Move all terms containing g to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + 3x = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 3x = 0 + 23 3x = 0 + 23 Combine like terms: 0 + 23 = 23 3x = 23 Add '-3x' to each side of the equation. 3x + -3x = 23 + -3x Combine like terms: 3x + -3x = 0 0 = 23 + -3x Simplifying 0 = 23 + -3x 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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