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Simplifying logx + log(x + 2) = log(6x + 1) Reorder the terms: glox + glo(2 + x) = log(6x + 1) glox + (2 * glo + x * glo) = log(6x + 1) glox + (2glo + glox) = log(6x + 1) Reorder the terms: 2glo + glox + glox = log(6x + 1) Combine like terms: glox + glox = 2glox 2glo + 2glox = log(6x + 1) Reorder the terms: 2glo + 2glox = glo(1 + 6x) 2glo + 2glox = (1 * glo + 6x * glo) 2glo + 2glox = (1glo + 6glox) Solving 2glo + 2glox = 1glo + 6glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-1glo' to each side of the equation. 2glo + -1glo + 2glox = 1glo + -1glo + 6glox Combine like terms: 2glo + -1glo = 1glo 1glo + 2glox = 1glo + -1glo + 6glox Combine like terms: 1glo + -1glo = 0 1glo + 2glox = 0 + 6glox 1glo + 2glox = 6glox Add '-6glox' to each side of the equation. 1glo + 2glox + -6glox = 6glox + -6glox Combine like terms: 2glox + -6glox = -4glox 1glo + -4glox = 6glox + -6glox Combine like terms: 6glox + -6glox = 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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