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