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