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