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Simplifying log(6x + -8) + -1log(8x) = 3 Reorder the terms: glo(-8 + 6x) + -1log(8x) = 3 (-8 * glo + 6x * glo) + -1log(8x) = 3 (-8glo + 6glox) + -1log(8x) = 3 Remove parenthesis around (8x) -8glo + 6glox + -1glo * 8x = 3 Reorder the terms for easier multiplication: -8glo + 6glox + -1 * 8glo * x = 3 Multiply -1 * 8 -8glo + 6glox + -8glo * x = 3 Multiply glo * x -8glo + 6glox + -8glox = 3 Combine like terms: 6glox + -8glox = -2glox -8glo + -2glox = 3 Solving -8glo + -2glox = 3 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Reorder the terms: -3 + -8glo + -2glox = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -8glo + -2glox = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(3 + 8glo + 2glox) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + 8glo + 2glox)' equal to zero and attempt to solve: Simplifying 3 + 8glo + 2glox = 0 Solving 3 + 8glo + 2glox = 0 Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + 8glo + -3 + 2glox = 0 + -3 Reorder the terms: 3 + -3 + 8glo + 2glox = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 8glo + 2glox = 0 + -3 8glo + 2glox = 0 + -3 Combine like terms: 0 + -3 = -3 8glo + 2glox = -3 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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