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Simplifying log(6x + 1) = log(x + 4) + log(2) Reorder the terms: glo(1 + 6x) = log(x + 4) + log(2) (1 * glo + 6x * glo) = log(x + 4) + log(2) (1glo + 6glox) = log(x + 4) + log(2) Reorder the terms: 1glo + 6glox = glo(4 + x) + log(2) 1glo + 6glox = (4 * glo + x * glo) + log(2) 1glo + 6glox = (4glo + glox) + log(2) Reorder the terms for easier multiplication: 1glo + 6glox = 4glo + glox + 2glo Reorder the terms: 1glo + 6glox = 4glo + 2glo + glox Combine like terms: 4glo + 2glo = 6glo 1glo + 6glox = 6glo + glox Solving 1glo + 6glox = 6glo + glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-6glo' to each side of the equation. 1glo + -6glo + 6glox = 6glo + -6glo + glox Combine like terms: 1glo + -6glo = -5glo -5glo + 6glox = 6glo + -6glo + glox Combine like terms: 6glo + -6glo = 0 -5glo + 6glox = 0 + glox -5glo + 6glox = glox Add '-1glox' to each side of the equation. -5glo + 6glox + -1glox = glox + -1glox Combine like terms: 6glox + -1glox = 5glox -5glo + 5glox = glox + -1glox Combine like terms: glox + -1glox = 0 -5glo + 5glox = 0 Factor out the Greatest Common Factor (GCF), '5glo'. 5glo(-1 + x) = 0 Ignore the factor 5.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 '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Add '-1x' to each side of the equation. x + -1x = 1 + -1x Combine like terms: x + -1x = 0 0 = 1 + -1x Simplifying 0 = 1 + -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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