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Simplifying log[12](x2 + -7) = log[12](x + 5) Reorder the terms: glo * 12(-7 + x2) = log[12](x + 5) Reorder the terms for easier multiplication: 12glo(-7 + x2) = log[12](x + 5) (-7 * 12glo + x2 * 12glo) = log[12](x + 5) (-84glo + 12glox2) = log[12](x + 5) Reorder the terms: -84glo + 12glox2 = glo * 12(5 + x) Reorder the terms for easier multiplication: -84glo + 12glox2 = 12glo(5 + x) -84glo + 12glox2 = (5 * 12glo + x * 12glo) -84glo + 12glox2 = (60glo + 12glox) Solving -84glo + 12glox2 = 60glo + 12glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-60glo' to each side of the equation. -84glo + -60glo + 12glox2 = 60glo + -60glo + 12glox Combine like terms: -84glo + -60glo = -144glo -144glo + 12glox2 = 60glo + -60glo + 12glox Combine like terms: 60glo + -60glo = 0 -144glo + 12glox2 = 0 + 12glox -144glo + 12glox2 = 12glox Add '-12glox' to each side of the equation. -144glo + -12glox + 12glox2 = 12glox + -12glox Combine like terms: 12glox + -12glox = 0 -144glo + -12glox + 12glox2 = 0 Factor out the Greatest Common Factor (GCF), '12glo'. 12glo(-12 + -1x + x2) = 0 Factor a trinomial. 12glo((-3 + -1x)(4 + -1x)) = 0 Ignore the factor 12.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 '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Add 'x' to each side of the equation. -1x + x = 3 + x Combine like terms: -1x + x = 0 0 = 3 + x Simplifying 0 = 3 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Add 'x' to each side of the equation. -1x + x = -4 + x Combine like terms: -1x + x = 0 0 = -4 + x Simplifying 0 = -4 + x 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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