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