Simplify: log 6(216) + [ log(42) - log(6) ] / log(49)

Sure, let's break this down:

1. Simplify the terms inside the brackets first: log(42) - log(6). According to the properties of logarithms, this can be rewritten as log(42/6) = log(7).

2. Now, substitute this back into the original equation: log 6(216) + log(7) / log(49).

3. Simplify log 6(216). 216 is 6^3, so log 6(216) simplifies to 3.

4. Substitute this back into the equation: 3 + log(7) / log(49).

5. Simplify log(7) / log(49). This is equivalent to log base 49 of 7, which simplifies to 1/2 (since 49 is 7^2).

6. Substitute this back into the equation: 3 + 1/2 = 3.5.

So, log 6(216) + [ log(42) - log(6) ] / log(49) simplifies to 3.5.