I don't understand the question at all...

L = 1/2 log r + 1/3 log s - 1/4 log t

Use Power Rule of Logarithms:

L = log(r^(1/2)) + log(s^(1/3)) - log(t^(1/4))

Use Multiplication Rule of Logarithms:

L = log( (r^(1/2)) * (s^(1/3)) ) - log(t^(1/4))

Use Quotient Rule of Logarithms:

L = log( ( (r^(1/2)) * (s^(1/3)) ) / (t^(1/4)) )