Lösungen

1

1000 x - x

x = 32.81468468468468468468468468468468468468468468;
y = 1000 x - x

z = y // Chop// Rationalize;  z

Clear[x];
Solve[1000 x - x == z, {x}] // Flatten

Remove["Global`*"]

2

Ln[x_]:=Log[x]; Ln[E]

Log[3,2^(Log[4,b])] Ln[9] / Ln[b] - Log[x,x/x^(Ln[a]) a^(Ln[x])]+1

u=Log[3,2^(Log[4,b])] Ln[9] / Ln[b] - Log[x,x/x^(Ln[a]) a^(Ln[x])]+1 //Simplify

u=u/.{Log[4]->2 Log[2], Log[9]->2 Log[3]}

u/.b->E

Remove["Global`*"]

3

Lg[x_]:=Log[10,x]; Lg[100]

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

ScientificForm[10000000000.]

Remove["Global`*"]

4

Lg[x_]:=Log[10,x];

Solve[{10 == y^(Lg[Sqrt[y]]), Lg[x+2]+Lg[x-5] == Lg[x-1]+Lg[2-x]}, {x,y}]

Remove["Global`*"]

5

Ln[x_]:=Log[x];

Ln[x^5]+6 /. {Log[x^5]->5 Log[x]}

Solve[0 == (Ln[x]^2+Ln[x^5]+6 /. {Log[x^5]->5 Log[x]}), {x}]

Remove["Global`*"]

6

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

Simplify[%]

% // N

FactorInteger[253125]

3^4 5^5

FactorInteger[2025]

(4 Log[3] + 5 Log[5]-2 Log[2])/(4 Log[3] + 2 Log[5]- Log[2])

% // N

1+ (3 Log[5]-Log[2])/(4 Log[3] + 2 Log[5]- Log[2])

% // N

Remove["Global`*"]

7

Solve[18+16 u+16 u x +32 x^2==0, {x}]

Solve[-9 - 8 u + (u^2) == 0, {u}]

Remove["Global`*"]

8

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

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

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

Remove["Global`*"]

9

Solve[Abs[s^2-2]==12,{s}]

Remove["Global`*"]

10

Solve[{
2a1+5a2-3a3==0,
4a1-2a2==6,
4a1-4a2+a3==7},{a1,a2,a3}] // Flatten

Erste Gleichung -5 statt +5 bei a2:

Solve[{
2a1-5a2-3a3==0,
4a1-2a2==6,
4a1-4a2+a3==7},{a1,a2,a3}] // Flatten

Remove["Global`*"]

11

M = {}