Lösungen

1

100 x - x

x = 145.27978787878787878787878787878787878787878787878;
y = 100 x - x

z = y // Chop// Rationalize;  z

Clear[x];
Solve[100 x - x == z, {x}] // Flatten

N[(4794233/33000), 200]

Remove["Global`*"]

2

?Log

Log[5, 10^(Log[5, c])] Log[5, 100]/Log[5, c] + 
        Log[x, x/x^(Log[5, c]) c^(Log[5, x])] // Simplify

(Log[5,10^(Log[5,c])] Log[5,100] / Log[5,c] + Log[x,x/x^(Log[5,c]) c^(Log[5,x])]//Simplify)/. Log[10^(Log[c]/Log[5])]-> (Log[c]/Log[5]) Log[10]

((Log[5, 10^(Log[5, c])] Log[5, 100]/Log[5, c] + 
                Log[x, x/x^(Log[5, c]) c^(Log[5, x])] // 
              Simplify) /. 
          Log[10^(Log[c]/Log[5])] -> (Log[c]/Log[5]) Log[
                10]) /. Log[100] -> 2 Log[10]

(((Log[5, 10^(Log[5, c])] Log[5, 100]/Log[5, c] + 
                    Log[x, x/x^(Log[5, c]) c^(Log[5, x])] // 
                  Simplify) /. 
              Log[10^(Log[c]/Log[5])] -> (Log[c]/Log[5]) Log[
                    10]) /. Log[100] -> 2 Log[10]) /. 
      Log[10] -> (Log[2] + Log[5])

%//N

Remove["Global`*"]

3

Lg[x_]:=Log[5,x]; Lg[25]

Solve[(1-Lg[Lg[x]])(Lg[Lg[x]]+1)==0,{x}]

N[%]

FactorInteger[3125]

Remove["Global`*"]

4

Lg[x_]:=Log[2,x];

Solve[{8 == y^(Lg[Sqrt[x]]), Lg[x+2]+Lg[x-5] == Lg[x+5]+Lg[2-x]}, {x,y}]

% // N

2 - 3.16228

Remove["Global`*"]

Lösung nicht zulässig, da  Lg[2-x] = Lg[-1.16228]  im Reellen nicht existiert.

5

Ln[x_]:=Log[x];

Ln[x^6]+6 /. {Log[x^6]->6 Log[x]}

solv=Solve[(Ln[x]^3+(Ln[x^6])/6==-6 Ln[x] /. {Log[x^6]->6 Log[x]}), {Log[x]}]//Flatten

Solve[Log[x] == 0, {x}]

Vergleich:

solv = 
      Solve[(Ln[x]^3 - (Ln[x^6])^2/6 == -6 Ln[x] /. {Log[
                    x^6] -> 6 Log[x]}), {Log[x]}] // 
        Flatten

% // N

solv[[1]]

E^0

(Hold[E^Log[x]] /. solv[[2]])[[1]]

% // N

(Hold[E^Log[x]] /. solv[[3]])[[1]]

% // N

Remove["Global`*"]

6

Solve[2^(3(x-1)) 3^(2x) 5^(1+2x) == 4^(6-3x),{x}]

Direkte Berechnung der Lösung erfolglos.

2^(3 (x - 1)) 3^(2  x) 5^(1 + 2  x) - 
        4^(6 - 3  x) // Simplify

(E^Log[2])^(3 (x - 1)) (E^Log[3])^(2  x) (E^
                Log[5])^(1 + 2  x) - (E^Log[4])^(6 - 3  x) // 
      Simplify

Solve[
        E^(Log[2] 3 (x - 1) + Log[3] 2  x + Log[5] (1 + 2  x)) == 
          E^(Log[4] (6 - 3  x)), {x}] // Simplify

2^15

FactorInteger[115200]

2^9 3^2 5^2

N[%]

Solve[(Log[2] 3 (x - 1) + Log[3] 2  x + 
              Log[5] (1 + 2  x)) == (Log[4] (6 - 3  x)), {x}] // 
      Simplify

N[%]

Plot[
        2^(3 (x - 1)) 3^(2  x) 5^(1 + 2  x) - 
          4^(6 - 3  x), {x, -1.1, 1.5}];

Plot[
        2^(3 (x - 1)) 3^(2  x) 5^(1 + 2  x) - 
          4^(6 - 3  x), {x, 0.5, 1}];

Remove["Global`*"]

7

Solve[9+8 u+8 u x +9 x^2==0, {x}]

Solve[-81 - 72 u + 16 (u^2) == 0, {u}]

% // N

Remove["Global`*"]

8

Solve[(Sqrt[x^2+4]+6x+2)/Sqrt[(x+2)]==0,{x}]

Solve[(Sqrt[x^2+4]+6x+2)==0,{x}]

N[%]

Plot[(Sqrt[x^2+4]+6x+2)/Sqrt[(x+2)],{x,-2,5}];

Remove["Global`*"]

9

Solve[Abs[s-2] Abs[s+2]==6+s,{s}]

% // N

Plot[Abs[s - 2] Abs[s + 2] - 6 - s, {s, -4, 5}];

Remove["Global`*"]

10

Solve[{
4x+2y-5z==0,
2x-3y==6,
32x-24y-15 z==8},{x,y,z}] // Flatten

Solve[{4  x + 2  y - 5  z == 0, 2  x - 3  y == 6, 
          32  x - 24  y - 16 z == 8}, {x, y, z}] // Flatten

% // N

Remove["Global`*"]

11

M = { }