Solve[{v*c == x 10^(2.72 - 6080/833),
   v*n == 10^(2.45 - 7830/833) (1 - x), (x*12.011) (0.2 - v) == (0.0218 -
       c) 50.9414, (0.2 - v) ((1 - x)*14.0067) == (0.0024 - n) 50.9414, 0 < v < 0.15,
   0 < c < 0.015, 0 < n < 0.003, 0 < x < 1}, {v, c, x, n}] // Chop
(*{{v -> 0.0998355, c -> 0.000241101, x -> 0.912861, n -> 9.79873*10^-8}}*)

3Â¥: Originally posted by xzczd at 2015-06-19 11:11:43
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Solve // Chop
(*{{v  ...

eqn = {Log[10, v*c/x] == 2.72 - 6080/833,
   Log[10, v*n/(1 - x)] == 2.45 - 7830/833, (0.2 - v)/(0.0218 - c) ==
    50.9414/(x*12.011), (0.2 - v)/(0.0024 - n) == 50.9414/((1 - x)*14.0067)};

Solve[eqn, {v, n, x, c}]

(*{{v -> -0.00107112, n -> -4.55851*10^-6, x -> 0.956507,
  c -> -0.0235467}, {v -> 0.0998355, n -> 9.79873*10^-8, x -> 0.912861,
  c -> 0.000241101}, {v -> -2.13445*10^-6, n -> -0.0526894, x -> -0.00177142,
  c -> 0.0218835}, {v -> 0.20005, n -> -0.000101436, x -> 181.756, c -> 0.0239569}}*)

4Â¥: Originally posted by xzczd at 2015-06-19 11:28:28
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eqn = {Log == 2.72 - 6080/833,
   Log == 2.45 - 7830/833, (0.2 - v)/(0.0218 - c) ==
    50.9414/(x*12.011), (0 ...

eqn = {Log[10, v*c/x] == 2.72 - 6080/T,
   Log[10, v*n/(1 - x)] == 2.45 - 7830/T, (m - v)/(0.0218 - c) ==
    50.9414/(x*12.011), (m - v)/(0.0024 - n) == 50.9414/((1 - x)*14.0067)};

Pick[#, And @@ {0 < v < 0.15, 0 < c < 0.015, 0 < n < 0.003, 0 < x < 1} /. #] & /@ Solve[eqn, {v, n, x, c}]

(* {{v -> 0.0998355, n -> 9.79873*10^-8, x -> 0.912861, c -> 0.000241101}} *)