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Simplifying log(8)(x2 + -14) = log(8)(5x) Reorder the terms: glo * 8(-14 + x2) = log(8)(5x) Reorder the terms for easier multiplication: 8glo(-14 + x2) = log(8)(5x) (-14 * 8glo + x2 * 8glo) = log(8)(5x) (-112glo + 8glox2) = log(8)(5x) Remove parenthesis around (5x) -112glo + 8glox2 = glo * 8 * 5x Reorder the terms for easier multiplication: -112glo + 8glox2 = 8 * 5glo * x Multiply 8 * 5 -112glo + 8glox2 = 40glo * x Multiply glo * x -112glo + 8glox2 = 40glox Solving -112glo + 8glox2 = 40glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-40glox' to each side of the equation. -112glo + -40glox + 8glox2 = 40glox + -40glox Combine like terms: 40glox + -40glox = 0 -112glo + -40glox + 8glox2 = 0 Factor out the Greatest Common Factor (GCF), '8glo'. 8glo(-14 + -5x + x2) = 0 Factor a trinomial. 8glo((-2 + -1x)(7 + -1x)) = 0 Ignore the factor 8.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 '(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. The solution to this equation could not be determined.
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