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Simplifying log[5](x * x + -17) = log[5](x + 3) Multiply x * x glo * 5(x2 + -17) = log[5](x + 3) Reorder the terms: glo * 5(-17 + x2) = log[5](x + 3) Reorder the terms for easier multiplication: 5glo(-17 + x2) = log[5](x + 3) (-17 * 5glo + x2 * 5glo) = log[5](x + 3) (-85glo + 5glox2) = log[5](x + 3) Reorder the terms: -85glo + 5glox2 = glo * 5(3 + x) Reorder the terms for easier multiplication: -85glo + 5glox2 = 5glo(3 + x) -85glo + 5glox2 = (3 * 5glo + x * 5glo) -85glo + 5glox2 = (15glo + 5glox) Solving -85glo + 5glox2 = 15glo + 5glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-15glo' to each side of the equation. -85glo + -15glo + 5glox2 = 15glo + -15glo + 5glox Combine like terms: -85glo + -15glo = -100glo -100glo + 5glox2 = 15glo + -15glo + 5glox Combine like terms: 15glo + -15glo = 0 -100glo + 5glox2 = 0 + 5glox -100glo + 5glox2 = 5glox Add '-5glox' to each side of the equation. -100glo + -5glox + 5glox2 = 5glox + -5glox Combine like terms: 5glox + -5glox = 0 -100glo + -5glox + 5glox2 = 0 Factor out the Greatest Common Factor (GCF), '5glo'. 5glo(-20 + -1x + x2) = 0 Factor a trinomial. 5glo((-4 + -1x)(5 + -1x)) = 0 Ignore the factor 5.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 '(-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.Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Add 'x' to each side of the equation. -1x + x = -5 + x Combine like terms: -1x + x = 0 0 = -5 + x Simplifying 0 = -5 + 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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