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Simplifying log(-11x + 2) = log(x2 + 30) Reorder the terms: glo(2 + -11x) = log(x2 + 30) (2 * glo + -11x * glo) = log(x2 + 30) (2glo + -11glox) = log(x2 + 30) Reorder the terms: 2glo + -11glox = glo(30 + x2) 2glo + -11glox = (30 * glo + x2 * glo) 2glo + -11glox = (30glo + glox2) Solving 2glo + -11glox = 30glo + glox2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-30glo' to each side of the equation. 2glo + -30glo + -11glox = 30glo + -30glo + glox2 Combine like terms: 2glo + -30glo = -28glo -28glo + -11glox = 30glo + -30glo + glox2 Combine like terms: 30glo + -30glo = 0 -28glo + -11glox = 0 + glox2 -28glo + -11glox = glox2 Add '-1glox2' to each side of the equation. -28glo + -11glox + -1glox2 = glox2 + -1glox2 Combine like terms: glox2 + -1glox2 = 0 -28glo + -11glox + -1glox2 = 0 Factor out the Greatest Common Factor (GCF), '-1glo'. -1glo(28 + 11x + x2) = 0 Factor a trinomial. -1glo((7 + x)(4 + x)) = 0 Ignore the factor -1.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 '(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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