I think I would be inclined to just take the logarithm directly:
log(Wf^t)= log(Qb^t)
log(W)+ log(f^t)= log(Q)+ log(b^t)
log(W)+ t log(f)= log(Q)+ t log(b)
log(W)+ t log(f)- t log)b)= log(Q)
t(log(f)- log(b)= log(Q)- log(W)
t log(f/b)= log(Q/W)
t= log(Q/W)/log(f/b)