Let's analyze and solve the two logarithmic expressions presented in the image:

Problem 5: $5 \log_5 2$

To solve this:

1. The logarithmic part, $\log_5 2$, means "the power to which 5 must be raised to get 2." This doesn't simplify directly, so let's leave it in logarithmic form for now.
2. The entire expression is $5 \times \log_5 2$. We can leave the logarithm as is, and the final expression is just $5 \log_5 2$.

For an approximation: $\log_5 2 = \frac{\log 2}{\log 5} \approx \frac{0.3010}{0.69897} \approx 0.43067$ Multiplying by 5: $5 \times 0.43067 \approx 2.15335$ So the approximate value is 2.15.

Problem 6: $\log 1$

For any base $b$, $\log_b 1 = 0$, because any number raised to the power of 0 equals 1: $b^0 = 1$ So, the value of $\log 1$ is 0.

Would you like more details or have any questions on these solutions?

Here are some related questions to deepen your understanding:

1. What is the general form of the logarithmic equation?
2. How do you convert between different logarithmic bases?
3. Why is the logarithm of 1 always 0, regardless of the base?
4. How can logarithms be used in solving exponential equations?
5. What is the change of base formula for logarithms?

Tip: Always remember that $\log_b b = 1$, because a number raised to the power of 1 is itself.