I'm studying for an algorithms final. There are some sample questions that I'd like to know how to solve. No calculators are permitted, and the methods used are more relevant to computer science than algebra. I'll try to be as specific as possible, because researching this has only led me to change-of-base formulas that require a calculator.
What is (approximately) the Log base 2 of 130,000,000?
What is (approximately) the Log base 4 of 1,000,000?
I'd also appreciate it if someone would explain base conversions without a calculator to me. Thank you. If this post is inappropriate, I'll remove it without hesitation.
Edit: Answers delivered in log(x)/log(r) will not be considered correct. Thank you.
What you need to do is make your own table during the exam.
2, 4, 8, 32, 64, 128, 256,512, 1024, ....
Find the power of 2 that is closest to the value you looking for. If you are asked for Log2(1000), you'd see the closest is 1024 (2**10): Ans: 10.