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Simplifying log(6x + 2) = log(x + 2) + log(7) Reorder the terms: glo(2 + 6x) = log(x + 2) + log(7) (2 * glo + 6x * glo) = log(x + 2) + log(7) (2glo + 6glox) = log(x + 2) + log(7) Reorder the terms: 2glo + 6glox = glo(2 + x) + log(7) 2glo + 6glox = (2 * glo + x * glo) + log(7) 2glo + 6glox = (2glo + glox) + log(7) Reorder the terms for easier multiplication: 2glo + 6glox = 2glo + glox + 7glo Reorder the terms: 2glo + 6glox = 2glo + 7glo + glox Combine like terms: 2glo + 7glo = 9glo 2glo + 6glox = 9glo + glox Solving 2glo + 6glox = 9glo + glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-9glo' to each side of the equation. 2glo + -9glo + 6glox = 9glo + -9glo + glox Combine like terms: 2glo + -9glo = -7glo -7glo + 6glox = 9glo + -9glo + glox Combine like terms: 9glo + -9glo = 0 -7glo + 6glox = 0 + glox -7glo + 6glox = glox Add '-1glox' to each side of the equation. -7glo + 6glox + -1glox = glox + -1glox Combine like terms: 6glox + -1glox = 5glox -7glo + 5glox = glox + -1glox Combine like terms: glox + -1glox = 0 -7glo + 5glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-7 + 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 '(-7 + 5x)' equal to zero and attempt to solve: Simplifying -7 + 5x = 0 Solving -7 + 5x = 0 Move all terms containing g to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + 5x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 5x = 0 + 7 5x = 0 + 7 Combine like terms: 0 + 7 = 7 5x = 7 Add '-5x' to each side of the equation. 5x + -5x = 7 + -5x Combine like terms: 5x + -5x = 0 0 = 7 + -5x Simplifying 0 = 7 + -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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