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Simplifying log[3](x + -5) = log[3](3x + -25) Reorder the terms: glo * 3(-5 + x) = log[3](3x + -25) Reorder the terms for easier multiplication: 3glo(-5 + x) = log[3](3x + -25) (-5 * 3glo + x * 3glo) = log[3](3x + -25) (-15glo + 3glox) = log[3](3x + -25) Reorder the terms: -15glo + 3glox = glo * 3(-25 + 3x) Reorder the terms for easier multiplication: -15glo + 3glox = 3glo(-25 + 3x) -15glo + 3glox = (-25 * 3glo + 3x * 3glo) -15glo + 3glox = (-75glo + 9glox) Solving -15glo + 3glox = -75glo + 9glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '75glo' to each side of the equation. -15glo + 75glo + 3glox = -75glo + 75glo + 9glox Combine like terms: -15glo + 75glo = 60glo 60glo + 3glox = -75glo + 75glo + 9glox Combine like terms: -75glo + 75glo = 0 60glo + 3glox = 0 + 9glox 60glo + 3glox = 9glox Add '-9glox' to each side of the equation. 60glo + 3glox + -9glox = 9glox + -9glox Combine like terms: 3glox + -9glox = -6glox 60glo + -6glox = 9glox + -9glox Combine like terms: 9glox + -9glox = 0 60glo + -6glox = 0 Factor out the Greatest Common Factor (GCF), '6glo'. 6glo(10 + -1x) = 0 Ignore the factor 6.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 '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Add 'x' to each side of the equation. -1x + x = -10 + x Combine like terms: -1x + x = 0 0 = -10 + x Simplifying 0 = -10 + 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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