The problem asks us to evaluate four expressions: 1. $log_5 0.2$

1. Problem Description

The problem asks us to evaluate four expressions:

1. $log_5 0.2$

2. $log_{10} 0.1$

3. $e^{ln \pi}$

4. $e^{ln \sqrt{5}}$

2. Solution Steps

1. $log_5 0.2$

Since $0.2 = \frac{1}{5} = 5^{-1}$, we have

$log_5 0.2 = log_5 5^{-1} = -1$

2. $log_{10} 0.1$

Since $0.1 = \frac{1}{10} = 10^{-1}$, we have

$log_{10} 0.1 = log_{10} 10^{-1} = -1$

3. $e^{ln \pi}$

Using the property that $e^{ln x} = x$, we have

$e^{ln \pi} = \pi$

4. $e^{ln \sqrt{5}}$

Using the property that $e^{ln x} = x$, we have

$e^{ln \sqrt{5}} = \sqrt{5}$

3. Final Answer

1. $log_5 0.2 = -1$

2. $log_{10} 0.1 = -1$

3. $e^{ln \pi} = \pi$

4. $e^{ln \sqrt{5}} = \sqrt{5}$