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Simplifying log[5](x + -8) = -1log[5](x + -4) Reorder the terms: glo * 5(-8 + x) = -1log[5](x + -4) Reorder the terms for easier multiplication: 5glo(-8 + x) = -1log[5](x + -4) (-8 * 5glo + x * 5glo) = -1log[5](x + -4) (-40glo + 5glox) = -1log[5](x + -4) Reorder the terms: -40glo + 5glox = -1glo * 5(-4 + x) Reorder the terms for easier multiplication: -40glo + 5glox = -1 * 5glo(-4 + x) Multiply -1 * 5 -40glo + 5glox = -5glo(-4 + x) -40glo + 5glox = (-4 * -5glo + x * -5glo) -40glo + 5glox = (20glo + -5glox) Solving -40glo + 5glox = 20glo + -5glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-20glo' to each side of the equation. -40glo + -20glo + 5glox = 20glo + -20glo + -5glox Combine like terms: -40glo + -20glo = -60glo -60glo + 5glox = 20glo + -20glo + -5glox Combine like terms: 20glo + -20glo = 0 -60glo + 5glox = 0 + -5glox -60glo + 5glox = -5glox Add '5glox' to each side of the equation. -60glo + 5glox + 5glox = -5glox + 5glox Combine like terms: 5glox + 5glox = 10glox -60glo + 10glox = -5glox + 5glox Combine like terms: -5glox + 5glox = 0 -60glo + 10glox = 0 Factor out the Greatest Common Factor (GCF), '10glo'. 10glo(-6 + x) = 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 '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Add '-1x' to each side of the equation. x + -1x = 6 + -1x Combine like terms: x + -1x = 0 0 = 6 + -1x Simplifying 0 = 6 + -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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