Questions about class of problems that can be solved with unlimited computational power, but access to only logarithmically many bits of the input?
It is contained in $P/Poly$

Let $M$ be a logarithmic time superoracle machine which decides some language $L$ in your class. We can define it by adding a special tape in which we can specify our desired language by writing some real number. Upon querying the oracle it will determine the membership of the given string to the specified language.

With polynomial length advice, you could provide the choice tree that determines what bits are read from a length $n$ input (if the first bit is x then go read y...). The questions to the oracles are determined by the bits read, and I can ask only a logarithmic number of questions (would work for polynomial too).

In the advice i could also hardcode a table which links any possible logarithmic input to the answers from the desired oracles. Given such advice and some input $x$, read the required bits using the choice tree, and simulate the special machine with the oracle answers given in the advice.