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Simplifying log(x + -7) + log(x + -5) = -1log(5) Reorder the terms: glo(-7 + x) + log(x + -5) = -1log(5) (-7 * glo + x * glo) + log(x + -5) = -1log(5) (-7glo + glox) + log(x + -5) = -1log(5) Reorder the terms: -7glo + glox + glo(-5 + x) = -1log(5) -7glo + glox + (-5 * glo + x * glo) = -1log(5) -7glo + glox + (-5glo + glox) = -1log(5) Reorder the terms: -7glo + -5glo + glox + glox = -1log(5) Combine like terms: -7glo + -5glo = -12glo -12glo + glox + glox = -1log(5) Combine like terms: glox + glox = 2glox -12glo + 2glox = -1log(5) Reorder the terms for easier multiplication: -12glo + 2glox = -1 * 5glo Multiply -1 * 5 -12glo + 2glox = -5glo Solving -12glo + 2glox = -5glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '5glo' to each side of the equation. -12glo + 5glo + 2glox = -5glo + 5glo Combine like terms: -12glo + 5glo = -7glo -7glo + 2glox = -5glo + 5glo Combine like terms: -5glo + 5glo = 0 -7glo + 2glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-7 + 2x) = 0Subproblem 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 '(-7 + 2x)' equal to zero and attempt to solve: Simplifying -7 + 2x = 0 Solving -7 + 2x = 0 Move all terms containing g to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + 2x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 2x = 0 + 7 2x = 0 + 7 Combine like terms: 0 + 7 = 7 2x = 7 Add '-2x' to each side of the equation. 2x + -2x = 7 + -2x Combine like terms: 2x + -2x = 0 0 = 7 + -2x Simplifying 0 = 7 + -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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