To solve $\log_6 \frac{3}{7}$ using the provided values, we can apply the property of logarithms:

$\log_b \frac{a}{c} = \log_b a - \log_b c$

In this case:

$\log_6 \frac{3}{7} = \log_6 3 - \log_6 7$

Given:

• $\log_6 3 \approx 0.613$
• $\log_6 7 \approx 1.086$

Substitute these values into the expression:

$\log_6 \frac{3}{7} \approx 0.613 - 1.086 = -0.473$

So, the approximate value of $\log_6 \frac{3}{7}$ is -0.473.

Would you like further details, or have any questions?

Here are some related questions for practice:

1. How would you evaluate $\log_6 \frac{7}{3}$ using the same properties?
2. What is the value of $\log_6 21$ given $\log_6 3$ and $\log_6 7$?
3. How can you use the change of base formula to verify these calculations?
4. If $\log_6 9$ is needed, how would you use $\log_6 3$ to find it?
5. What is the approximate value of $\log_6 49$?

Tip: Memorizing key logarithmic properties, like the quotient, product, and power rules, can make solving these problems much easier.