Question

How do you determine values for a and b that satisfy the double inequality `3<log_a(b)<4`?

Answer 1

In base a, your number must be between `a^3` and `a^4`.

Explanation:

For example, if your base was 10, your numbers would be between 1000 and 10,000. In interval notation, (1000,10000).
Check: `log_10(1234)~~3.09`

In base 2, they should be between (8,16).
Check: `log_2(14)~~3.81`

Try any other base to make sure!