Let's evaluate the given logarithmic expressions from the image.

(a) $\log_6 6$

The logarithmic expression $\log_6 6$ means: "To what power must 6 be raised to get 6?"

Since $6^1 = 6$, the value is:

$\log_6 6 = 1$

(b) $\log_4 \left(\frac{1}{64}\right)$

The logarithmic expression $\log_4 \left(\frac{1}{64}\right)$ asks: "To what power must 4 be raised to get $\frac{1}{64}$?"

We know that: $4^3 = 64 \quad \text{so} \quad 4^{-3} = \frac{1}{64}$

Thus: $\log_4 \left(\frac{1}{64}\right) = -3$

Final answers:

• (a) $\log_6 6 = 1$
• (b) $\log_4 \left(\frac{1}{64}\right) = -3$

Would you like further details or clarifications?

Here are 5 related questions to practice:

1. What is $\log_5 25$?
2. What is $\log_3 27$?
3. How do you simplify $\log_2 8$?
4. Find $\log_7 49$.
5. What is $\log_9 \left(\frac{1}{81}\right)$?

Tip: Remember, $\log_b a = x$ means $b^x = a$.