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Simplifying log(3x + 4) + -1log(15x + 4) = 1 + -1log(5x + -4) Reorder the terms: glo(4 + 3x) + -1log(15x + 4) = 1 + -1log(5x + -4) (4 * glo + 3x * glo) + -1log(15x + 4) = 1 + -1log(5x + -4) (4glo + 3glox) + -1log(15x + 4) = 1 + -1log(5x + -4) Reorder the terms: 4glo + 3glox + -1glo(4 + 15x) = 1 + -1log(5x + -4) 4glo + 3glox + (4 * -1glo + 15x * -1glo) = 1 + -1log(5x + -4) 4glo + 3glox + (-4glo + -15glox) = 1 + -1log(5x + -4) Reorder the terms: 4glo + -4glo + 3glox + -15glox = 1 + -1log(5x + -4) Combine like terms: 4glo + -4glo = 0 0 + 3glox + -15glox = 1 + -1log(5x + -4) 3glox + -15glox = 1 + -1log(5x + -4) Combine like terms: 3glox + -15glox = -12glox -12glox = 1 + -1log(5x + -4) Reorder the terms: -12glox = 1 + -1glo(-4 + 5x) -12glox = 1 + (-4 * -1glo + 5x * -1glo) -12glox = 1 + (4glo + -5glox) Solving -12glox = 1 + 4glo + -5glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-4glo' to each side of the equation. -4glo + -12glox = 1 + 4glo + -4glo + -5glox Combine like terms: 4glo + -4glo = 0 -4glo + -12glox = 1 + 0 + -5glox -4glo + -12glox = 1 + -5glox Add '5glox' to each side of the equation. -4glo + -12glox + 5glox = 1 + -5glox + 5glox Combine like terms: -12glox + 5glox = -7glox -4glo + -7glox = 1 + -5glox + 5glox Combine like terms: -5glox + 5glox = 0 -4glo + -7glox = 1 + 0 -4glo + -7glox = 1 Reorder the terms: -1 + -4glo + -7glox = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -4glo + -7glox = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 4glo + 7glox) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 4glo + 7glox)' equal to zero and attempt to solve: Simplifying 1 + 4glo + 7glox = 0 Solving 1 + 4glo + 7glox = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 4glo + -1 + 7glox = 0 + -1 Reorder the terms: 1 + -1 + 4glo + 7glox = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4glo + 7glox = 0 + -1 4glo + 7glox = 0 + -1 Combine like terms: 0 + -1 = -1 4glo + 7glox = -1 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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