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Simplifying log(5x + 1) = log(2x + 4) Reorder the terms: glo(1 + 5x) = log(2x + 4) (1 * glo + 5x * glo) = log(2x + 4) (1glo + 5glox) = log(2x + 4) Reorder the terms: 1glo + 5glox = glo(4 + 2x) 1glo + 5glox = (4 * glo + 2x * glo) 1glo + 5glox = (4glo + 2glox) Solving 1glo + 5glox = 4glo + 2glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-4glo' to each side of the equation. 1glo + -4glo + 5glox = 4glo + -4glo + 2glox Combine like terms: 1glo + -4glo = -3glo -3glo + 5glox = 4glo + -4glo + 2glox Combine like terms: 4glo + -4glo = 0 -3glo + 5glox = 0 + 2glox -3glo + 5glox = 2glox Add '-2glox' to each side of the equation. -3glo + 5glox + -2glox = 2glox + -2glox Combine like terms: 5glox + -2glox = 3glox -3glo + 3glox = 2glox + -2glox Combine like terms: 2glox + -2glox = 0 -3glo + 3glox = 0 Factor out the Greatest Common Factor (GCF), '3glo'. 3glo(-1 + x) = 0 Ignore the factor 3.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 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Add '-1x' to each side of the equation. x + -1x = 1 + -1x Combine like terms: x + -1x = 0 0 = 1 + -1x Simplifying 0 = 1 + -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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