To solve $\log_6 2 + \log_6 18$, we can use the property of logarithms that states:

$\log_b a + \log_b c = \log_b (a \cdot c)$

Applying this property:

$\log_6 2 + \log_6 18 = \log_6 (2 \cdot 18)$

Calculating $2 \cdot 18$:

$2 \cdot 18 = 36$

So,

$\log_6 2 + \log_6 18 = \log_6 36$

Now, since $6^2 = 36$, we can simplify further:

$\log_6 36 = 2$

Therefore, the answer is:

$\log_6 2 + \log_6 18 = 2$

Would you like a deeper explanation of the properties used here or have any questions?

Additional Questions for Practice

1. How would you simplify $\log_6 3 + \log_6 12$?
2. What is $\log_3 27$ using basic logarithmic properties?
3. How would you evaluate $\log_5 25 + \log_5 4$?
4. Can you expand $\log_6 (36 \cdot 18)$ using properties of logarithms?
5. How do you express $\log_b a^2$ in terms of simpler logarithmic forms?

Tip

Always look for properties that allow you to combine or break down logarithmic expressions to simplify complex logarithmic equations.