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

1 Answer
Jan 21, 2017

Answer:

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!