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Simplifying log(7x + -9) = log(x + 2) + log(8) Reorder the terms: glo(-9 + 7x) = log(x + 2) + log(8) (-9 * glo + 7x * glo) = log(x + 2) + log(8) (-9glo + 7glox) = log(x + 2) + log(8) Reorder the terms: -9glo + 7glox = glo(2 + x) + log(8) -9glo + 7glox = (2 * glo + x * glo) + log(8) -9glo + 7glox = (2glo + glox) + log(8) Reorder the terms for easier multiplication: -9glo + 7glox = 2glo + glox + 8glo Reorder the terms: -9glo + 7glox = 2glo + 8glo + glox Combine like terms: 2glo + 8glo = 10glo -9glo + 7glox = 10glo + glox Solving -9glo + 7glox = 10glo + glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-10glo' to each side of the equation. -9glo + -10glo + 7glox = 10glo + -10glo + glox Combine like terms: -9glo + -10glo = -19glo -19glo + 7glox = 10glo + -10glo + glox Combine like terms: 10glo + -10glo = 0 -19glo + 7glox = 0 + glox -19glo + 7glox = glox Add '-1glox' to each side of the equation. -19glo + 7glox + -1glox = glox + -1glox Combine like terms: 7glox + -1glox = 6glox -19glo + 6glox = glox + -1glox Combine like terms: glox + -1glox = 0 -19glo + 6glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-19 + 6x) = 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 '(-19 + 6x)' equal to zero and attempt to solve: Simplifying -19 + 6x = 0 Solving -19 + 6x = 0 Move all terms containing g to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + 6x = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 6x = 0 + 19 6x = 0 + 19 Combine like terms: 0 + 19 = 19 6x = 19 Add '-6x' to each side of the equation. 6x + -6x = 19 + -6x Combine like terms: 6x + -6x = 0 0 = 19 + -6x Simplifying 0 = 19 + -6x 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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