(log(3) 2 + 3log(3) 1/4)/(log(3) 20 - log(3) 5)

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First, let's simplify the expression step by step:

log3 2 = log3 2

log3 1/4 = log3 4^-1 = -1

Therefore, the expression becomes:

(log3 2 + 3(-1))/(log3 20 - log3 5)

Now, we simplify further:

(log3 2 - 3)/(log3 20 - log3 5)

Now, we use the properties of logarithms to combine the terms in the numerator and denominator:

log3 2 - 3 = log3 2/20 = log3 1/10

log3 20 - log3 5 = log3 20/5 = log3 4

Therefore, the expression simplifies to:

log3 1/10 / log3 4 = log4 1/10 = log4 10^-1 = -1

So, the final simplified expression is -1.