Question

What is the value of `log_2 5` between two consecutive integers?

Answer 1

`2 < log_2 5 < 3`

Explanation:

Note that `log_2 x` is a strictly monotonically increasing function from `(0, oo)` onto `(-oo, oo)`

We find:

`2^2 = 4 < 5 < 8 = 2^3`

Since `log_2` is a strictly monotonically increasing function, we can take the logarithm base `2` of all parts of this inequality to get:

`2 = log_2 4 < log_2 5 < log_2 8 = 3`