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Simplifying log[4](2x) = log[4](35 + -1x2) Remove parenthesis around (2x) glo * 4 * 2x = log[4](35 + -1x2) Reorder the terms for easier multiplication: 4 * 2glo * x = log[4](35 + -1x2) Multiply 4 * 2 8glo * x = log[4](35 + -1x2) Multiply glo * x 8glox = log[4](35 + -1x2) Reorder the terms for easier multiplication: 8glox = 4glo(35 + -1x2) 8glox = (35 * 4glo + -1x2 * 4glo) 8glox = (140glo + -4glox2) Solving 8glox = 140glo + -4glox2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-140glo' to each side of the equation. -140glo + 8glox = 140glo + -140glo + -4glox2 Combine like terms: 140glo + -140glo = 0 -140glo + 8glox = 0 + -4glox2 -140glo + 8glox = -4glox2 Add '4glox2' to each side of the equation. -140glo + 8glox + 4glox2 = -4glox2 + 4glox2 Combine like terms: -4glox2 + 4glox2 = 0 -140glo + 8glox + 4glox2 = 0 Factor out the Greatest Common Factor (GCF), '4glo'. 4glo(-35 + 2x + x2) = 0 Factor a trinomial. 4glo((-7 + -1x)(5 + -1x)) = 0 Ignore the factor 4.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 + -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 '(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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