🖥️ Veni. Vidi. sudo rm -rf / vici.

1. $$(\log_2 64 = 6), denn (2^6=64)$$
2. $$(\log_2 1024 = 10), denn (2^{10}=1024)$$
3. $$(\log_2 1 = 0), denn (2^0=1)$$
4. $$(\log_2 \frac18 = -3), denn (2^{-3}=\frac18)$$
5. $$(\log_2 \frac1{16} = -4), denn (2^{-4}=\frac1{16})$$
6. $$(\log_2 \frac1{128} = -7), denn (2^{-7}=\frac1{128})$$
7. $$(\log_2 \sqrt2 = \frac12), denn (2^{1/2}=\sqrt2)$$
8. $$(\log_2 2^{13} = 13)$$

$$ \boxed{6;\ 10;\ 0;\ -3;\ -4;\ -7;\ \frac12;\ 13} $$

1. $$(\log_3 9 = 2), denn (3^2=9)$$
2. $$(\log_3 1 = 0), denn (3^0=1)$$
3. $$(\log_3 243 = 5), denn (3^5=243)$$
4. $$(\log_3 \frac1{81} = -4), denn (3^{-4}=\frac1{81})$$
5. $$(\log_3 \frac19 = -2), denn (3^{-2}=\frac19)$$
6. $$(\log_3 3^7 = 7)$$
7. $$(\log_3 \sqrt3 = \frac12), denn (3^{1/2}=\sqrt3)$$
8. $$(\log3 \sqrt{3^3} = \log3(3^{3/2})=\frac32)$$

$$ \boxed{2;\ 0;\ 5;\ -4;\ -2;\ 7;\ \frac12;\ \frac32} $$

1. $$(\log_4 4 = 1), denn (4^1=4)$$
2. $$(\log_4 16 = 2), denn (4^2=16)$$
3. $$(\log_4 1 = 0), denn (4^0=1)$$
4. $$(\log_4 256 = 4), denn (4^4=256)$$
5. $$(\log_4 4^5 = 5)$$
6. $$(\log4 0{,}25 = \log4 \frac14 = -1), denn (4^{-1}=\frac14)$$
7. $$(\log4 0{,}0625 = \log4 \frac1{16} = -2), denn (4^{-2}=\frac1{16})$$
8. $$(\log_4 2 = \frac12), denn (4^{1/2}=2)$$

$$ \boxed{1;\ 2;\ 0;\ 4;\ 5;\ -1;\ -2;\ \frac12} $$

$$ \boxed{6,\ 10,\ 0,\ -3,\ -4,\ -7,\ \frac12,\ 13} $$

$$ \boxed{2,\ 0,\ 5,\ -4,\ -2,\ 7,\ \frac12,\ \frac32} $$

$$ \boxed{1,\ 2,\ 0,\ 4,\ 5,\ -1,\ -2,\ \frac12} $$