`log_2 (1/8)` Evaluate the expression without using a calculator.

`log_2 (1/8)`

To evaluate this, consider the base and argument of the logarithm. The base of the logarithm is 2. And the 8 can be expressed in terms of factor 2. So factoring 8, the expression becomes:

`= log_2 (1/2^3)`

Then, apply the negative exponent rule `a^(-m)=1/a^m` .

`= log_2 (2^(-3))`

To simplify this further, apply the logarithmic rule `log_b (a^m) = m * log_b (a)` .

`= -3 * log_2(2)`

Take note that when the base and argument of a logarithm are the same, the resulting value is 1 `(log_b (b) = 1)` .

`= - 3 * 1`

`= -3`

Therefore, `log_2 (1/8) = -3` .