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Simplifying log(4x + 1) = log(x + 4) + log(3) Reorder the terms: glo(1 + 4x) = log(x + 4) + log(3) (1 * glo + 4x * glo) = log(x + 4) + log(3) (1glo + 4glox) = log(x + 4) + log(3) Reorder the terms: 1glo + 4glox = glo(4 + x) + log(3) 1glo + 4glox = (4 * glo + x * glo) + log(3) 1glo + 4glox = (4glo + glox) + log(3) Reorder the terms for easier multiplication: 1glo + 4glox = 4glo + glox + 3glo Reorder the terms: 1glo + 4glox = 4glo + 3glo + glox Combine like terms: 4glo + 3glo = 7glo 1glo + 4glox = 7glo + glox Solving 1glo + 4glox = 7glo + glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-7glo' to each side of the equation. 1glo + -7glo + 4glox = 7glo + -7glo + glox Combine like terms: 1glo + -7glo = -6glo -6glo + 4glox = 7glo + -7glo + glox Combine like terms: 7glo + -7glo = 0 -6glo + 4glox = 0 + glox -6glo + 4glox = glox Add '-1glox' to each side of the equation. -6glo + 4glox + -1glox = glox + -1glox Combine like terms: 4glox + -1glox = 3glox -6glo + 3glox = glox + -1glox Combine like terms: glox + -1glox = 0 -6glo + 3glox = 0 Factor out the Greatest Common Factor (GCF), '3glo'. 3glo(-2 + 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 '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Add '-1x' to each side of the equation. x + -1x = 2 + -1x Combine like terms: x + -1x = 0 0 = 2 + -1x Simplifying 0 = 2 + -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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