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Simplifying log(2x + -1) + log(x + 2) = loh(8x + -4) Reorder the terms: glo(-1 + 2x) + log(x + 2) = loh(8x + -4) (-1 * glo + 2x * glo) + log(x + 2) = loh(8x + -4) (-1glo + 2glox) + log(x + 2) = loh(8x + -4) Reorder the terms: -1glo + 2glox + glo(2 + x) = loh(8x + -4) -1glo + 2glox + (2 * glo + x * glo) = loh(8x + -4) -1glo + 2glox + (2glo + glox) = loh(8x + -4) Reorder the terms: -1glo + 2glo + 2glox + glox = loh(8x + -4) Combine like terms: -1glo + 2glo = 1glo 1glo + 2glox + glox = loh(8x + -4) Combine like terms: 2glox + glox = 3glox 1glo + 3glox = loh(8x + -4) Reorder the terms: 1glo + 3glox = hlo(-4 + 8x) 1glo + 3glox = (-4 * hlo + 8x * hlo) 1glo + 3glox = (-4hlo + 8hlox) Solving 1glo + 3glox = -4hlo + 8hlox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Reorder the terms: 1glo + 3glox + 4hlo + -8hlox = -4hlo + 4hlo + 8hlox + -8hlox Combine like terms: -4hlo + 4hlo = 0 1glo + 3glox + 4hlo + -8hlox = 0 + 8hlox + -8hlox 1glo + 3glox + 4hlo + -8hlox = 8hlox + -8hlox Combine like terms: 8hlox + -8hlox = 0 1glo + 3glox + 4hlo + -8hlox = 0 Factor out the Greatest Common Factor (GCF), 'lo'. lo(g + 3gx + 4h + -8hx) = 0Subproblem 1
Set the factor 'lo' equal to zero and attempt to solve: Simplifying lo = 0 Solving lo = 0 Move all terms containing g to the left, all other terms to the right. Add '-1lo' to each side of the equation. lo + -1lo = 0 + -1lo Remove the zero: 0 = -1lo Simplifying 0 = -1lo 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 '(g + 3gx + 4h + -8hx)' equal to zero and attempt to solve: Simplifying g + 3gx + 4h + -8hx = 0 Solving g + 3gx + 4h + -8hx = 0 Move all terms containing g to the left, all other terms to the right. Add '-4h' to each side of the equation. g + 3gx + 4h + -4h + -8hx = 0 + -4h Combine like terms: 4h + -4h = 0 g + 3gx + 0 + -8hx = 0 + -4h g + 3gx + -8hx = 0 + -4h Remove the zero: g + 3gx + -8hx = -4h Add '8hx' to each side of the equation. g + 3gx + -8hx + 8hx = -4h + 8hx Combine like terms: -8hx + 8hx = 0 g + 3gx + 0 = -4h + 8hx g + 3gx = -4h + 8hx 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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