Logarithmagic!!!!

\[\log_a(b)\] is like asking: \[a^\text{what} = b\]

1. \(\log_2(8)\)
2. \(\log_2(16)\)
3. \(\log_2\left(\frac12\right)\)
4. \(\log_3(9)\)
5. \(\log_3(27)\)
6. \(\log_3(81)\)
7. \(\log_4(64)\)
8. \(\log_4(16)\)
9. \(\log_4(32)\)
10. \(\log_7(49)\)
11. \(\log_{49}(7)\)
12. \(\log_7\left(\frac{1}{49}\right)\)
13. \(\log_{1/49}\left(7\right)\)
14. \(\log_{1/49}\left(\frac17\right)\)
15. \(\log_5(25)\)
16. \(\log_5(1)\)
17. \(\log_5\left(\frac{1}{25}\right)\)
18. \(\log_6(36)\)
19. \(\log_6(216)\)
20. \(\log_{216}(6)\)
21. \(\log_{1/3}(9)\)
22. \(\log_3(-9)\)
23. \(\log_{1/3}(-9)\)
24. \(\log_{10}(10,000)\)
25. \(\log_{1/2}\left(\frac14\right)\)
26. \(\log_{\frac{3}{2}}\left(\frac{4}{9}\right)\)
27. \(\log_{10}(0.00000000000001)\)
28. \(\log_{4}(-64)\)
29. \(\log_{4}\left(1/16\right)\)
30. \(\log_{4}\left(128\right)\)
31. \(\log_{\frac{1}{16}}(2)\)
32. \(\log_{2025}(1)\)
33. \(\log_{2025}(45)\)
34. \(\log_{5\sqrt[3]{5}}(25)\)
35. \(\log_{8192}(2)\)
36. \(\log_{8192}(4)\)
37. \(\log_5(-25)\)
38. \(\log_7(0)\)
39. \(\log_7(1)\)
40. \(\log_9(243)\)
41. \(\log_{125}(0.0016)\)
42. \(\log_{512}(1/2)\)
43. \(\log_7(50)\)
44. \(\log_{12}(100)\)
45. \(\log_{3\sqrt3}\left(729\right)\)
46. \(\log_{4\sqrt[3]{2}}(32)\)
47. \(\log_{2}(3000)\)
48. \(\log_{a+b}\left(a^2+2ab+b^2\right)\)
49. \(\log_{a-b}\left(a^2-2ab+b^2\right)\)
50. \(\log_{a+b}\left(a^3+3a^2b+3ab^2 + b^3\right)\)
51. \(\log_{a+b}\left(a^6 \!+\! 6 a^5 b \!+\! 15 a^4 b^2 + 20 a^3 b^3 \!+\! 15 a^2 b^4 \!+\! 6 a b^5 \!+\! b^6 \right)\)
52. \(\displaystyle \log_{a^3b^4}\left(\frac{b^{-12}}{(\sqrt[4]{a^3})^{12}}\right)\)
53. \(\displaystyle \log_{\frac{7}{\left(qr^3\right)^9}}\left(\frac{q^{18}r^{24}}{49}\right)\)
54. \(\displaystyle \log_{\frac{x^2\sqrt{b}}{y^3} }\left(\left( \frac{y^2}{x^3} \right)^4\cdot\frac{y^{10}}{b^3} \right)\)