Question: User: log (8) 5
1. **Stating the problem:**
We need to evaluate $\log_5(8)$, which means finding the exponent to which we raise $5$ to get $8$.
2. **Formula used:**
The logarithm definition is:
$$\log_b(a) = x \iff b^x = a$$
Here, $b=5$ and $a=8$.
3. **Using change of base formula:**
Since $\log_5(8)$ is not straightforward, we use the change of base formula:
$$\log_5(8) = \frac{\log_{10}(8)}{\log_{10}(5)}$$
or using natural logarithm:
$$\log_5(8) = \frac{\ln(8)}{\ln(5)}$$
4. **Calculate the values:**
Using approximate values:
$$\ln(8) \approx 2.0794$$
$$\ln(5) \approx 1.6094$$
5. **Divide:**
$$\log_5(8) = \frac{2.0794}{1.6094}$$
6. **Simplify:**
$$\log_5(8) \approx 1.292$$
**Final answer:**
$$\boxed{1.292}$$