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Simplifying log(x2 + 6x) = log(7) Reorder the terms: glo(6x + x2) = log(7) (6x * glo + x2 * glo) = log(7) (6glox + glox2) = log(7) Reorder the terms for easier multiplication: 6glox + glox2 = 7glo Solving 6glox + glox2 = 7glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-7glo' to each side of the equation. 6glox + -7glo + glox2 = 7glo + -7glo Reorder the terms: -7glo + 6glox + glox2 = 7glo + -7glo Combine like terms: 7glo + -7glo = 0 -7glo + 6glox + glox2 = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-7 + 6x + x2) = 0 Factor a trinomial. glo((-7 + -1x)(1 + -1x)) = 0Subproblem 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 + -1x)' equal to zero and attempt to solve: Simplifying -7 + -1x = 0 Solving -7 + -1x = 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 + -1x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1x = 0 + 7 -1x = 0 + 7 Combine like terms: 0 + 7 = 7 -1x = 7 Add 'x' to each side of the equation. -1x + x = 7 + x Combine like terms: -1x + x = 0 0 = 7 + x Simplifying 0 = 7 + x 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 '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Add 'x' to each side of the equation. -1x + x = -1 + x Combine like terms: -1x + x = 0 0 = -1 + x Simplifying 0 = -1 + 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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