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Simplifying log(3x + -8) + -1log(4x) + 5 = 7 Reorder the terms: glo(-8 + 3x) + -1log(4x) + 5 = 7 (-8 * glo + 3x * glo) + -1log(4x) + 5 = 7 (-8glo + 3glox) + -1log(4x) + 5 = 7 Remove parenthesis around (4x) -8glo + 3glox + -1glo * 4x + 5 = 7 Reorder the terms for easier multiplication: -8glo + 3glox + -1 * 4glo * x + 5 = 7 Multiply -1 * 4 -8glo + 3glox + -4glo * x + 5 = 7 Multiply glo * x -8glo + 3glox + -4glox + 5 = 7 Reorder the terms: 5 + -8glo + 3glox + -4glox = 7 Combine like terms: 3glox + -4glox = -1glox 5 + -8glo + -1glox = 7 Solving 5 + -8glo + -1glox = 7 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -8glo + -5 + -1glox = 7 + -5 Reorder the terms: 5 + -5 + -8glo + -1glox = 7 + -5 Combine like terms: 5 + -5 = 0 0 + -8glo + -1glox = 7 + -5 -8glo + -1glox = 7 + -5 Combine like terms: 7 + -5 = 2 -8glo + -1glox = 2 Reorder the terms: -2 + -8glo + -1glox = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -8glo + -1glox = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 8glo + glox) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 8glo + glox)' equal to zero and attempt to solve: Simplifying 2 + 8glo + glox = 0 Solving 2 + 8glo + glox = 0 Move all terms containing g to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + 8glo + -2 + glox = 0 + -2 Reorder the terms: 2 + -2 + 8glo + glox = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 8glo + glox = 0 + -2 8glo + glox = 0 + -2 Combine like terms: 0 + -2 = -2 8glo + glox = -2 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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