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

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Answer 1 · 2017-01-21T21:18:24

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

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!

How do you determine values for a and b that satisfy the double inequality 3<log_a(b)<43<log_a(b)<4?