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Simplifying log(7)(x2) = log(7)(3x + 10) Reorder the terms for easier multiplication: 7glo * x2 = log(7)(3x + 10) Multiply glo * x2 7glox2 = log(7)(3x + 10) Reorder the terms: 7glox2 = glo * 7(10 + 3x) Reorder the terms for easier multiplication: 7glox2 = 7glo(10 + 3x) 7glox2 = (10 * 7glo + 3x * 7glo) 7glox2 = (70glo + 21glox) Solving 7glox2 = 70glo + 21glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-70glo' to each side of the equation. -70glo + 7glox2 = 70glo + -70glo + 21glox Combine like terms: 70glo + -70glo = 0 -70glo + 7glox2 = 0 + 21glox -70glo + 7glox2 = 21glox Add '-21glox' to each side of the equation. -70glo + -21glox + 7glox2 = 21glox + -21glox Combine like terms: 21glox + -21glox = 0 -70glo + -21glox + 7glox2 = 0 Factor out the Greatest Common Factor (GCF), '7glo'. 7glo(-10 + -3x + x2) = 0 Factor a trinomial. 7glo((-2 + -1x)(5 + -1x)) = 0 Ignore the factor 7.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 '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Add 'x' to each side of the equation. -1x + x = 2 + x Combine like terms: -1x + x = 0 0 = 2 + x Simplifying 0 = 2 + 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 '(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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