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Simplifying log5(x + 2) = log5(3x + -8) Reorder the terms: g5lo(2 + x) = log5(3x + -8) (2 * g5lo + x * g5lo) = log5(3x + -8) (2g5lo + g5lox) = log5(3x + -8) Reorder the terms: 2g5lo + g5lox = g5lo(-8 + 3x) 2g5lo + g5lox = (-8 * g5lo + 3x * g5lo) 2g5lo + g5lox = (-8g5lo + 3g5lox) Solving 2g5lo + g5lox = -8g5lo + 3g5lox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '8g5lo' to each side of the equation. 2g5lo + 8g5lo + g5lox = -8g5lo + 8g5lo + 3g5lox Combine like terms: 2g5lo + 8g5lo = 10g5lo 10g5lo + g5lox = -8g5lo + 8g5lo + 3g5lox Combine like terms: -8g5lo + 8g5lo = 0 10g5lo + g5lox = 0 + 3g5lox 10g5lo + g5lox = 3g5lox Add '-3g5lox' to each side of the equation. 10g5lo + g5lox + -3g5lox = 3g5lox + -3g5lox Combine like terms: g5lox + -3g5lox = -2g5lox 10g5lo + -2g5lox = 3g5lox + -3g5lox Combine like terms: 3g5lox + -3g5lox = 0 10g5lo + -2g5lox = 0 Factor out the Greatest Common Factor (GCF), '2g5lo'. 2g5lo(5 + -1x) = 0 Ignore the factor 2.Subproblem 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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Add 'x' to each side of the equation. -1x + x = -5 + x Combine like terms: -1x + x = 0 0 = -5 + x Simplifying 0 = -5 + 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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