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Simplifying log(6x + 4) = log(x + 3) + log(5) Reorder the terms: glo(4 + 6x) = log(x + 3) + log(5) (4 * glo + 6x * glo) = log(x + 3) + log(5) (4glo + 6glox) = log(x + 3) + log(5) Reorder the terms: 4glo + 6glox = glo(3 + x) + log(5) 4glo + 6glox = (3 * glo + x * glo) + log(5) 4glo + 6glox = (3glo + glox) + log(5) Reorder the terms for easier multiplication: 4glo + 6glox = 3glo + glox + 5glo Reorder the terms: 4glo + 6glox = 3glo + 5glo + glox Combine like terms: 3glo + 5glo = 8glo 4glo + 6glox = 8glo + glox Solving 4glo + 6glox = 8glo + glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-8glo' to each side of the equation. 4glo + -8glo + 6glox = 8glo + -8glo + glox Combine like terms: 4glo + -8glo = -4glo -4glo + 6glox = 8glo + -8glo + glox Combine like terms: 8glo + -8glo = 0 -4glo + 6glox = 0 + glox -4glo + 6glox = glox Add '-1glox' to each side of the equation. -4glo + 6glox + -1glox = glox + -1glox Combine like terms: 6glox + -1glox = 5glox -4glo + 5glox = glox + -1glox Combine like terms: glox + -1glox = 0 -4glo + 5glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-4 + 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 '(-4 + 5x)' equal to zero and attempt to solve: Simplifying -4 + 5x = 0 Solving -4 + 5x = 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 + 5x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 5x = 0 + 4 5x = 0 + 4 Combine like terms: 0 + 4 = 4 5x = 4 Add '-5x' to each side of the equation. 5x + -5x = 4 + -5x Combine like terms: 5x + -5x = 0 0 = 4 + -5x Simplifying 0 = 4 + -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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