SOLUTION: Explain why log[base 40]3 is between ¼ and 1/3

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Question 997348: Explain why log[base 40]3 is between ¼ and 1/3
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Use change of base formula
log b (x)=log d (x)/log d (b)
use 3 as the new base
log 40 of 3= log 3 (3)/log 3 (40)
That is 1/log 3(40)
log 3(27)=3
log 3(81)=4
So log 3 (40) is between 3 and 4
1/log 3 (40) is between 1/3 and 1/4