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

Jan 21, 2017

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: ${\log}_{10} \left(1234\right) \approx 3.09$

In base 2, they should be between (8,16).
Check: ${\log}_{2} \left(14\right) \approx 3.81$

Try any other base to make sure!