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Simplifying log9(-11x + 2) = log9(x2 + 30) Reorder the terms: g9lo(2 + -11x) = log9(x2 + 30) (2 * g9lo + -11x * g9lo) = log9(x2 + 30) (2g9lo + -11g9lox) = log9(x2 + 30) Reorder the terms: 2g9lo + -11g9lox = g9lo(30 + x2) 2g9lo + -11g9lox = (30 * g9lo + x2 * g9lo) 2g9lo + -11g9lox = (30g9lo + g9lox2) Solving 2g9lo + -11g9lox = 30g9lo + g9lox2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-30g9lo' to each side of the equation. 2g9lo + -30g9lo + -11g9lox = 30g9lo + -30g9lo + g9lox2 Combine like terms: 2g9lo + -30g9lo = -28g9lo -28g9lo + -11g9lox = 30g9lo + -30g9lo + g9lox2 Combine like terms: 30g9lo + -30g9lo = 0 -28g9lo + -11g9lox = 0 + g9lox2 -28g9lo + -11g9lox = g9lox2 Add '-1g9lox2' to each side of the equation. -28g9lo + -11g9lox + -1g9lox2 = g9lox2 + -1g9lox2 Combine like terms: g9lox2 + -1g9lox2 = 0 -28g9lo + -11g9lox + -1g9lox2 = 0 Factor out the Greatest Common Factor (GCF), '-1g9lo'. -1g9lo(28 + 11x + x2) = 0 Factor a trinomial. -1g9lo((7 + x)(4 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor 'g9lo' equal to zero and attempt to solve: Simplifying g9lo = 0 Solving g9lo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying g9lo = 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 '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Add '-1x' to each side of the equation. x + -1x = -7 + -1x Combine like terms: x + -1x = 0 0 = -7 + -1x Simplifying 0 = -7 + -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
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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