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Simplifying log(x + 4) + log(2x + 3) = log(x + 2) Reorder the terms: glo(4 + x) + log(2x + 3) = log(x + 2) (4 * glo + x * glo) + log(2x + 3) = log(x + 2) (4glo + glox) + log(2x + 3) = log(x + 2) Reorder the terms: 4glo + glox + glo(3 + 2x) = log(x + 2) 4glo + glox + (3 * glo + 2x * glo) = log(x + 2) 4glo + glox + (3glo + 2glox) = log(x + 2) Reorder the terms: 4glo + 3glo + glox + 2glox = log(x + 2) Combine like terms: 4glo + 3glo = 7glo 7glo + glox + 2glox = log(x + 2) Combine like terms: glox + 2glox = 3glox 7glo + 3glox = log(x + 2) Reorder the terms: 7glo + 3glox = glo(2 + x) 7glo + 3glox = (2 * glo + x * glo) 7glo + 3glox = (2glo + glox) Solving 7glo + 3glox = 2glo + glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-2glo' to each side of the equation. 7glo + -2glo + 3glox = 2glo + -2glo + glox Combine like terms: 7glo + -2glo = 5glo 5glo + 3glox = 2glo + -2glo + glox Combine like terms: 2glo + -2glo = 0 5glo + 3glox = 0 + glox 5glo + 3glox = glox Add '-1glox' to each side of the equation. 5glo + 3glox + -1glox = glox + -1glox Combine like terms: 3glox + -1glox = 2glox 5glo + 2glox = glox + -1glox Combine like terms: glox + -1glox = 0 5glo + 2glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(5 + 2x) = 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 '(5 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 0 Move all terms containing g to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Add '-2x' to each side of the equation. 2x + -2x = -5 + -2x Combine like terms: 2x + -2x = 0 0 = -5 + -2x Simplifying 0 = -5 + -2x 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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