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Simplifying log5(x + 1) + log5(x + -3) = log5(x + 2) Reorder the terms: g5lo(1 + x) + log5(x + -3) = log5(x + 2) (1 * g5lo + x * g5lo) + log5(x + -3) = log5(x + 2) (1g5lo + g5lox) + log5(x + -3) = log5(x + 2) Reorder the terms: 1g5lo + g5lox + g5lo(-3 + x) = log5(x + 2) 1g5lo + g5lox + (-3 * g5lo + x * g5lo) = log5(x + 2) 1g5lo + g5lox + (-3g5lo + g5lox) = log5(x + 2) Reorder the terms: 1g5lo + -3g5lo + g5lox + g5lox = log5(x + 2) Combine like terms: 1g5lo + -3g5lo = -2g5lo -2g5lo + g5lox + g5lox = log5(x + 2) Combine like terms: g5lox + g5lox = 2g5lox -2g5lo + 2g5lox = log5(x + 2) Reorder the terms: -2g5lo + 2g5lox = g5lo(2 + x) -2g5lo + 2g5lox = (2 * g5lo + x * g5lo) -2g5lo + 2g5lox = (2g5lo + g5lox) Solving -2g5lo + 2g5lox = 2g5lo + g5lox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-2g5lo' to each side of the equation. -2g5lo + -2g5lo + 2g5lox = 2g5lo + -2g5lo + g5lox Combine like terms: -2g5lo + -2g5lo = -4g5lo -4g5lo + 2g5lox = 2g5lo + -2g5lo + g5lox Combine like terms: 2g5lo + -2g5lo = 0 -4g5lo + 2g5lox = 0 + g5lox -4g5lo + 2g5lox = g5lox Add '-1g5lox' to each side of the equation. -4g5lo + 2g5lox + -1g5lox = g5lox + -1g5lox Combine like terms: 2g5lox + -1g5lox = 1g5lox -4g5lo + 1g5lox = g5lox + -1g5lox Combine like terms: g5lox + -1g5lox = 0 -4g5lo + 1g5lox = 0 Factor out the Greatest Common Factor (GCF), 'g5lo'. g5lo(-4 + x) = 0Subproblem 1
Set the factor 'g5lo' equal to zero and attempt to solve: Simplifying g5lo = 0 Solving g5lo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying g5lo = 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 '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Add '-1x' to each side of the equation. x + -1x = 4 + -1x Combine like terms: x + -1x = 0 0 = 4 + -1x Simplifying 0 = 4 + -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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