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Simplifying log[2](2x + 5) = log[7](x2 + 3x + 3) Reorder the terms: glo * 2(5 + 2x) = log[7](x2 + 3x + 3) Reorder the terms for easier multiplication: 2glo(5 + 2x) = log[7](x2 + 3x + 3) (5 * 2glo + 2x * 2glo) = log[7](x2 + 3x + 3) (10glo + 4glox) = log[7](x2 + 3x + 3) Reorder the terms: 10glo + 4glox = glo * 7(3 + 3x + x2) Reorder the terms for easier multiplication: 10glo + 4glox = 7glo(3 + 3x + x2) 10glo + 4glox = (3 * 7glo + 3x * 7glo + x2 * 7glo) 10glo + 4glox = (21glo + 21glox + 7glox2) Solving 10glo + 4glox = 21glo + 21glox + 7glox2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-21glo' to each side of the equation. 10glo + -21glo + 4glox = 21glo + 21glox + -21glo + 7glox2 Combine like terms: 10glo + -21glo = -11glo -11glo + 4glox = 21glo + 21glox + -21glo + 7glox2 Reorder the terms: -11glo + 4glox = 21glo + -21glo + 21glox + 7glox2 Combine like terms: 21glo + -21glo = 0 -11glo + 4glox = 0 + 21glox + 7glox2 -11glo + 4glox = 21glox + 7glox2 Add '-21glox' to each side of the equation. -11glo + 4glox + -21glox = 21glox + -21glox + 7glox2 Combine like terms: 4glox + -21glox = -17glox -11glo + -17glox = 21glox + -21glox + 7glox2 Combine like terms: 21glox + -21glox = 0 -11glo + -17glox = 0 + 7glox2 -11glo + -17glox = 7glox2 Add '-7glox2' to each side of the equation. -11glo + -17glox + -7glox2 = 7glox2 + -7glox2 Combine like terms: 7glox2 + -7glox2 = 0 -11glo + -17glox + -7glox2 = 0 Factor out the Greatest Common Factor (GCF), '-1glo'. -1glo(11 + 17x + 7x2) = 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 '(11 + 17x + 7x2)' equal to zero and attempt to solve: Simplifying 11 + 17x + 7x2 = 0 Solving 11 + 17x + 7x2 = 0 Move all terms containing g to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + 17x + -11 + 7x2 = 0 + -11 Reorder the terms: 11 + -11 + 17x + 7x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 17x + 7x2 = 0 + -11 17x + 7x2 = 0 + -11 Combine like terms: 0 + -11 = -11 17x + 7x2 = -11 Add '-17x' to each side of the equation. 17x + -17x + 7x2 = -11 + -17x Combine like terms: 17x + -17x = 0 0 + 7x2 = -11 + -17x 7x2 = -11 + -17x Add '-7x2' to each side of the equation. 7x2 + -7x2 = -11 + -17x + -7x2 Combine like terms: 7x2 + -7x2 = 0 0 = -11 + -17x + -7x2 Simplifying 0 = -11 + -17x + -7x2 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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