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Simplifying log4(2 + -1x) = log4(-5x + -18) (2 * g4lo + -1x * g4lo) = log4(-5x + -18) (2g4lo + -1g4lox) = log4(-5x + -18) Reorder the terms: 2g4lo + -1g4lox = g4lo(-18 + -5x) 2g4lo + -1g4lox = (-18 * g4lo + -5x * g4lo) 2g4lo + -1g4lox = (-18g4lo + -5g4lox) Solving 2g4lo + -1g4lox = -18g4lo + -5g4lox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '18g4lo' to each side of the equation. 2g4lo + 18g4lo + -1g4lox = -18g4lo + 18g4lo + -5g4lox Combine like terms: 2g4lo + 18g4lo = 20g4lo 20g4lo + -1g4lox = -18g4lo + 18g4lo + -5g4lox Combine like terms: -18g4lo + 18g4lo = 0 20g4lo + -1g4lox = 0 + -5g4lox 20g4lo + -1g4lox = -5g4lox Add '5g4lox' to each side of the equation. 20g4lo + -1g4lox + 5g4lox = -5g4lox + 5g4lox Combine like terms: -1g4lox + 5g4lox = 4g4lox 20g4lo + 4g4lox = -5g4lox + 5g4lox Combine like terms: -5g4lox + 5g4lox = 0 20g4lo + 4g4lox = 0 Factor out the Greatest Common Factor (GCF), '4g4lo'. 4g4lo(5 + x) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'g4lo' equal to zero and attempt to solve: Simplifying g4lo = 0 Solving g4lo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying g4lo = 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 '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Add '-1x' to each side of the equation. x + -1x = -5 + -1x Combine like terms: x + -1x = 0 0 = -5 + -1x Simplifying 0 = -5 + -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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