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Simplifying log(x + -4) + loga(x + 4) = log6x Reorder the terms: glo(-4 + x) + loga(x + 4) = log6x (-4 * glo + x * glo) + loga(x + 4) = log6x (-4glo + glox) + loga(x + 4) = log6x Reorder the terms: -4glo + glox + aglo(4 + x) = log6x -4glo + glox + (4 * aglo + x * aglo) = log6x -4glo + glox + (4aglo + aglox) = log6x Reorder the terms: 4aglo + aglox + -4glo + glox = log6x Solving 4aglo + aglox + -4glo + glox = g6lox Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4glo' to each side of the equation. 4aglo + aglox + -4glo + 4glo + glox = 4glo + g6lox Combine like terms: -4glo + 4glo = 0 4aglo + aglox + 0 + glox = 4glo + g6lox 4aglo + aglox + glox = 4glo + g6lox Add '-1glox' to each side of the equation. 4aglo + aglox + glox + -1glox = 4glo + -1glox + g6lox Combine like terms: glox + -1glox = 0 4aglo + aglox + 0 = 4glo + -1glox + g6lox 4aglo + aglox = 4glo + -1glox + g6lox Reorder the terms: 4aglo + aglox + -4glo + glox + -1g6lox = 4glo + -4glo + -1glox + glox + g6lox + -1g6lox Combine like terms: 4glo + -4glo = 0 4aglo + aglox + -4glo + glox + -1g6lox = 0 + -1glox + glox + g6lox + -1g6lox 4aglo + aglox + -4glo + glox + -1g6lox = -1glox + glox + g6lox + -1g6lox Combine like terms: -1glox + glox = 0 4aglo + aglox + -4glo + glox + -1g6lox = 0 + g6lox + -1g6lox 4aglo + aglox + -4glo + glox + -1g6lox = g6lox + -1g6lox Combine like terms: g6lox + -1g6lox = 0 4aglo + aglox + -4glo + glox + -1g6lox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(4a + ax + -4 + x + -1g5x) = 0Subproblem 1
Set the factor 'glo' equal to zero and attempt to solve: Simplifying glo = 0 Solving glo = 0 Move all terms containing a to the left, all other terms to the right. Add '-1glo' to each side of the equation. glo + -1glo = 0 + -1glo Remove the zero: 0 = -1glo Simplifying 0 = -1glo 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 '(4a + ax + -4 + x + -1g5x)' equal to zero and attempt to solve: Simplifying 4a + ax + -4 + x + -1g5x = 0 Reorder the terms: -4 + 4a + ax + -1g5x + x = 0 Solving -4 + 4a + ax + -1g5x + x = 0 Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4a + ax + -1g5x + 4 + x = 0 + 4 Reorder the terms: -4 + 4 + 4a + ax + -1g5x + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 4a + ax + -1g5x + x = 0 + 4 4a + ax + -1g5x + x = 0 + 4 Combine like terms: 0 + 4 = 4 4a + ax + -1g5x + x = 4 Add 'g5x' to each side of the equation. 4a + ax + -1g5x + g5x + x = 4 + g5x Combine like terms: -1g5x + g5x = 0 4a + ax + 0 + x = 4 + g5x 4a + ax + x = 4 + g5x Add '-1x' to each side of the equation. 4a + ax + x + -1x = 4 + g5x + -1x Combine like terms: x + -1x = 0 4a + ax + 0 = 4 + g5x + -1x 4a + ax = 4 + g5x + -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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