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Simplifying log(x + 5) = log(5x + 4) Reorder the terms: glo(5 + x) = log(5x + 4) (5 * glo + x * glo) = log(5x + 4) (5glo + glox) = log(5x + 4) Reorder the terms: 5glo + glox = glo(4 + 5x) 5glo + glox = (4 * glo + 5x * glo) 5glo + glox = (4glo + 5glox) Solving 5glo + glox = 4glo + 5glox 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. 5glo + -4glo + glox = 4glo + -4glo + 5glox Combine like terms: 5glo + -4glo = 1glo 1glo + glox = 4glo + -4glo + 5glox Combine like terms: 4glo + -4glo = 0 1glo + glox = 0 + 5glox 1glo + glox = 5glox Add '-5glox' to each side of the equation. 1glo + glox + -5glox = 5glox + -5glox Combine like terms: glox + -5glox = -4glox 1glo + -4glox = 5glox + -5glox Combine like terms: 5glox + -5glox = 0 1glo + -4glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(1 + -4x) = 0Subproblem 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 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 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 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Add '4x' to each side of the equation. -4x + 4x = -1 + 4x Combine like terms: -4x + 4x = 0 0 = -1 + 4x Simplifying 0 = -1 + 4x 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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