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Simplifying log(5x2 + 4) = 2log(3x2) + -1log(2x2 + -1) Reorder the terms: glo(4 + 5x2) = 2log(3x2) + -1log(2x2 + -1) (4 * glo + 5x2 * glo) = 2log(3x2) + -1log(2x2 + -1) (4glo + 5glox2) = 2log(3x2) + -1log(2x2 + -1) Remove parenthesis around (3x2) 4glo + 5glox2 = 2glo * 3x2 + -1log(2x2 + -1) Reorder the terms for easier multiplication: 4glo + 5glox2 = 2 * 3glo * x2 + -1log(2x2 + -1) Multiply 2 * 3 4glo + 5glox2 = 6glo * x2 + -1log(2x2 + -1) Multiply glo * x2 4glo + 5glox2 = 6glox2 + -1log(2x2 + -1) Reorder the terms: 4glo + 5glox2 = 6glox2 + -1glo(-1 + 2x2) 4glo + 5glox2 = 6glox2 + (-1 * -1glo + 2x2 * -1glo) 4glo + 5glox2 = 6glox2 + (1glo + -2glox2) Reorder the terms: 4glo + 5glox2 = 1glo + 6glox2 + -2glox2 Combine like terms: 6glox2 + -2glox2 = 4glox2 4glo + 5glox2 = 1glo + 4glox2 Solving 4glo + 5glox2 = 1glo + 4glox2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-1glo' to each side of the equation. 4glo + -1glo + 5glox2 = 1glo + -1glo + 4glox2 Combine like terms: 4glo + -1glo = 3glo 3glo + 5glox2 = 1glo + -1glo + 4glox2 Combine like terms: 1glo + -1glo = 0 3glo + 5glox2 = 0 + 4glox2 3glo + 5glox2 = 4glox2 Add '-4glox2' to each side of the equation. 3glo + 5glox2 + -4glox2 = 4glox2 + -4glox2 Combine like terms: 5glox2 + -4glox2 = 1glox2 3glo + 1glox2 = 4glox2 + -4glox2 Combine like terms: 4glox2 + -4glox2 = 0 3glo + 1glox2 = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(3 + x2) = 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 '(3 + x2)' equal to zero and attempt to solve: Simplifying 3 + x2 = 0 Solving 3 + x2 = 0 Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x2 = 0 + -3 x2 = 0 + -3 Combine like terms: 0 + -3 = -3 x2 = -3 Add '-1x2' to each side of the equation. x2 + -1x2 = -3 + -1x2 Combine like terms: x2 + -1x2 = 0 0 = -3 + -1x2 Simplifying 0 = -3 + -1x2 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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