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Simplifying 3log[5](x * x + -17) = log[5](x + 3) Multiply x * x 3glo * 5(x2 + -17) = log[5](x + 3) Reorder the terms: 3glo * 5(-17 + x2) = log[5](x + 3) Reorder the terms for easier multiplication: 3 * 5glo(-17 + x2) = log[5](x + 3) Multiply 3 * 5 15glo(-17 + x2) = log[5](x + 3) (-17 * 15glo + x2 * 15glo) = log[5](x + 3) (-255glo + 15glox2) = log[5](x + 3) Reorder the terms: -255glo + 15glox2 = glo * 5(3 + x) Reorder the terms for easier multiplication: -255glo + 15glox2 = 5glo(3 + x) -255glo + 15glox2 = (3 * 5glo + x * 5glo) -255glo + 15glox2 = (15glo + 5glox) Solving -255glo + 15glox2 = 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. -255glo + -15glo + 15glox2 = 15glo + -15glo + 5glox Combine like terms: -255glo + -15glo = -270glo -270glo + 15glox2 = 15glo + -15glo + 5glox Combine like terms: 15glo + -15glo = 0 -270glo + 15glox2 = 0 + 5glox -270glo + 15glox2 = 5glox Add '-5glox' to each side of the equation. -270glo + -5glox + 15glox2 = 5glox + -5glox Combine like terms: 5glox + -5glox = 0 -270glo + -5glox + 15glox2 = 0 Factor out the Greatest Common Factor (GCF), '5glo'. 5glo(-54 + -1x + 3x2) = 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 '(-54 + -1x + 3x2)' equal to zero and attempt to solve: Simplifying -54 + -1x + 3x2 = 0 Solving -54 + -1x + 3x2 = 0 Move all terms containing g to the left, all other terms to the right. Add '54' to each side of the equation. -54 + -1x + 54 + 3x2 = 0 + 54 Reorder the terms: -54 + 54 + -1x + 3x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + -1x + 3x2 = 0 + 54 -1x + 3x2 = 0 + 54 Combine like terms: 0 + 54 = 54 -1x + 3x2 = 54 Add 'x' to each side of the equation. -1x + x + 3x2 = 54 + x Combine like terms: -1x + x = 0 0 + 3x2 = 54 + x 3x2 = 54 + x Add '-3x2' to each side of the equation. 3x2 + -3x2 = 54 + x + -3x2 Combine like terms: 3x2 + -3x2 = 0 0 = 54 + x + -3x2 Simplifying 0 = 54 + x + -3x2 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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