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Simplifying log(5)(3x + 7) = -1log(5)(x + -5) Reorder the terms: glo * 5(7 + 3x) = -1log(5)(x + -5) Reorder the terms for easier multiplication: 5glo(7 + 3x) = -1log(5)(x + -5) (7 * 5glo + 3x * 5glo) = -1log(5)(x + -5) (35glo + 15glox) = -1log(5)(x + -5) Reorder the terms: 35glo + 15glox = -1glo * 5(-5 + x) Reorder the terms for easier multiplication: 35glo + 15glox = -1 * 5glo(-5 + x) Multiply -1 * 5 35glo + 15glox = -5glo(-5 + x) 35glo + 15glox = (-5 * -5glo + x * -5glo) 35glo + 15glox = (25glo + -5glox) Solving 35glo + 15glox = 25glo + -5glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-25glo' to each side of the equation. 35glo + -25glo + 15glox = 25glo + -25glo + -5glox Combine like terms: 35glo + -25glo = 10glo 10glo + 15glox = 25glo + -25glo + -5glox Combine like terms: 25glo + -25glo = 0 10glo + 15glox = 0 + -5glox 10glo + 15glox = -5glox Add '5glox' to each side of the equation. 10glo + 15glox + 5glox = -5glox + 5glox Combine like terms: 15glox + 5glox = 20glox 10glo + 20glox = -5glox + 5glox Combine like terms: -5glox + 5glox = 0 10glo + 20glox = 0 Factor out the Greatest Common Factor (GCF), '10glo'. 10glo(1 + 2x) = 0 Ignore the factor 10.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 '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Add '-2x' to each side of the equation. 2x + -2x = -1 + -2x Combine like terms: 2x + -2x = 0 0 = -1 + -2x Simplifying 0 = -1 + -2x 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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