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Simplifying log[5](x2 + -3x) = log[5](2x + 6) Reorder the terms: glo * 5(-3x + x2) = log[5](2x + 6) Reorder the terms for easier multiplication: 5glo(-3x + x2) = log[5](2x + 6) (-3x * 5glo + x2 * 5glo) = log[5](2x + 6) (-15glox + 5glox2) = log[5](2x + 6) Reorder the terms: -15glox + 5glox2 = glo * 5(6 + 2x) Reorder the terms for easier multiplication: -15glox + 5glox2 = 5glo(6 + 2x) -15glox + 5glox2 = (6 * 5glo + 2x * 5glo) -15glox + 5glox2 = (30glo + 10glox) Solving -15glox + 5glox2 = 30glo + 10glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-30glo' to each side of the equation. -15glox + -30glo + 5glox2 = 30glo + -30glo + 10glox Reorder the terms: -30glo + -15glox + 5glox2 = 30glo + -30glo + 10glox Combine like terms: 30glo + -30glo = 0 -30glo + -15glox + 5glox2 = 0 + 10glox -30glo + -15glox + 5glox2 = 10glox Add '-10glox' to each side of the equation. -30glo + -15glox + -10glox + 5glox2 = 10glox + -10glox Combine like terms: -15glox + -10glox = -25glox -30glo + -25glox + 5glox2 = 10glox + -10glox Combine like terms: 10glox + -10glox = 0 -30glo + -25glox + 5glox2 = 0 Factor out the Greatest Common Factor (GCF), '5glo'. 5glo(-6 + -5x + x2) = 0 Factor a trinomial. 5glo((-1 + -1x)(6 + -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 '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Add 'x' to each side of the equation. -1x + x = 1 + x Combine like terms: -1x + x = 0 0 = 1 + x Simplifying 0 = 1 + 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 '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 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 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Add 'x' to each side of the equation. -1x + x = -6 + x Combine like terms: -1x + x = 0 0 = -6 + x Simplifying 0 = -6 + 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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