To nine decimal places log2 = 0.3010299996 and log3 = 0.477121255.
(i) calculate log5 and log 6 to three decimal places.(no calculator)
(ii) by taking logs, or otherwise, show that 5* 10^47<3^100<6*10^47
(iii) hence write down the first digit of 3^100
(iv) find the first digit of each of the following numbers:2^1000, 2^10000 and 2^100000
I must stress that all these questions are difficult only because you can't use a calculator
If you can do these questions, I hereby declare that you're very clever