Without using technology, rank these logarithms in order from least to greatest: log₄62,log₆36,log₃10,log₅20. I'm not sure how to do this question because the bases are different. Thanks!

Answer 1

log₄62 = a , 4^a = 62 , I know 4^3 = 64 , so a = appr 3 , but a < 3
log₆36 = b , 6^b = 36, so b = 2
log₃10 = c , 3^c = 10, I know 3^2 = 10 , so c = appr 2, but c >2
log₅20 = d , 5^d = 20 , I know 4^2 = 25, so d < 2

order: log₅20 , log₆36 , log₃10 , log₄62