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Simplifying log(6x + 1) = log(x + 2) + log(5) Reorder the terms: glo(1 + 6x) = log(x + 2) + log(5) (1 * glo + 6x * glo) = log(x + 2) + log(5) (1glo + 6glox) = log(x + 2) + log(5) Reorder the terms: 1glo + 6glox = glo(2 + x) + log(5) 1glo + 6glox = (2 * glo + x * glo) + log(5) 1glo + 6glox = (2glo + glox) + log(5) Reorder the terms for easier multiplication: 1glo + 6glox = 2glo + glox + 5glo Reorder the terms: 1glo + 6glox = 2glo + 5glo + glox Combine like terms: 2glo + 5glo = 7glo 1glo + 6glox = 7glo + glox Solving 1glo + 6glox = 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 + 6glox = 7glo + -7glo + glox Combine like terms: 1glo + -7glo = -6glo -6glo + 6glox = 7glo + -7glo + glox Combine like terms: 7glo + -7glo = 0 -6glo + 6glox = 0 + glox -6glo + 6glox = glox Add '-1glox' to each side of the equation. -6glo + 6glox + -1glox = glox + -1glox Combine like terms: 6glox + -1glox = 5glox -6glo + 5glox = glox + -1glox Combine like terms: glox + -1glox = 0 -6glo + 5glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-6 + 5x) = 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 '(-6 + 5x)' equal to zero and attempt to solve: Simplifying -6 + 5x = 0 Solving -6 + 5x = 0 Move all terms containing g to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + 5x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 5x = 0 + 6 5x = 0 + 6 Combine like terms: 0 + 6 = 6 5x = 6 Add '-5x' to each side of the equation. 5x + -5x = 6 + -5x Combine like terms: 5x + -5x = 0 0 = 6 + -5x Simplifying 0 = 6 + -5x 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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