Lösungen

1

Schnitt: [-7,  (-4, 6), 8] 
  Vereinigung:  (-4, 1[, 6), Infinity)

Resultat:    (-4, Infinity)

2

Log[Log[E^c]] /. 
      Log[E^c_] -> c Log[E]

Log[Log[E^(2  c)]] /. Log[E^c_] -> c Log[E]

u = (Log[Log[E^c]] + Log[Log[E^(2  c)]] /. 
            Log[E^c_] -> c Log[E]) /. 
        Log[a_] + Log[b_] -> Log[a b]

v = ((c^Sqrt[8]) / (c^Sqrt[2]))^(Sqrt[2]/
              Sqrt[3]) /. (c_^a_)^b_ -> c^(a b)

u  + v // Simplify

3

f[x_, b_] := 2 x^2 + 3 b x  +  48

Solve[f[x, b] == 0, {x}]

Solve[(Sqrt[-128 + 3 (b^2)]) == 0, {b}]

N[%]

Plot[(Sqrt[-128 + 3 (b^2)]), {b, -10, 10}];

4

Solve[{
3 y  +  z  == 
          56, 
z - w == 
          42, 
2  x + y == 
          14, 
Sqrt[x^2] + w == 
          0
}, {x, y, z, w}]

5

Remove["Global`*"]

z = 23.71467467;
10^5 u == Floor[10^5  z]

10^2 u == Floor[10^2  z]

10^5 u - 10^2 u == Floor[10^5  z] - Floor[10^2  z]

Solve[
      10^5 u - 10^2 u == Floor[10^5  z] - Floor[10^2  z], {u}]

6

(1 - Log[12, Log[12, x]]) (Log[4, Log[3, x]] + 1) == 
      0

Simplify[(1 - Log[12, Log[12, x]]) (Log[4, Log[3, x]] + 
              1)] == 0

Solve[
      Simplify[(1 - Log[12, Log[12, x]]) (Log[4, Log[3, x]] + 
                1)] == 0, {x}]

7

Log[x^5] /. Log[a_^b_] -> b Log[a]

Solve[
      0 == 
        Evaluate[(Log[x])^2 + (Log[x^5] /. 
                Log[a_^b_] -> b Log[a]) + 6], {x}]

8

Sqrt[Sqrt[(s^2 + 2)^2]] == 1

Solve[Sqrt[Sqrt[(s^2 + 2)^2]] == 1, {s}]

Plot[Sqrt[Sqrt[(s^2 + 2)^2]], {s, -3, 3}, 
        PlotRange -> {0, 3.5}];

Keine Lösung