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Simplifying log(x + 6) = log(8x) + -1log(3x + 2) Reorder the terms: glo(6 + x) = log(8x) + -1log(3x + 2) (6 * glo + x * glo) = log(8x) + -1log(3x + 2) (6glo + glox) = log(8x) + -1log(3x + 2) Remove parenthesis around (8x) 6glo + glox = glo * 8x + -1log(3x + 2) Reorder the terms for easier multiplication: 6glo + glox = 8glo * x + -1log(3x + 2) Multiply glo * x 6glo + glox = 8glox + -1log(3x + 2) Reorder the terms: 6glo + glox = 8glox + -1glo(2 + 3x) 6glo + glox = 8glox + (2 * -1glo + 3x * -1glo) 6glo + glox = 8glox + (-2glo + -3glox) Reorder the terms: 6glo + glox = -2glo + 8glox + -3glox Combine like terms: 8glox + -3glox = 5glox 6glo + glox = -2glo + 5glox Solving 6glo + glox = -2glo + 5glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '2glo' to each side of the equation. 6glo + 2glo + glox = -2glo + 2glo + 5glox Combine like terms: 6glo + 2glo = 8glo 8glo + glox = -2glo + 2glo + 5glox Combine like terms: -2glo + 2glo = 0 8glo + glox = 0 + 5glox 8glo + glox = 5glox Add '-5glox' to each side of the equation. 8glo + glox + -5glox = 5glox + -5glox Combine like terms: glox + -5glox = -4glox 8glo + -4glox = 5glox + -5glox Combine like terms: 5glox + -5glox = 0 8glo + -4glox = 0 Factor out the Greatest Common Factor (GCF), '4glo'. 4glo(2 + -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 '(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. The solution to this equation could not be determined.
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