Universal Multi Head Turing Machine
No. The logarithmic overhead comes from the fact that the machine you're simulating could have an arbitrarily large state set&nbsp;$Q$ and arbitrarily large tape alphabet&nbsp;$\Gamma$. To simulate any such machine using a fixed, constant number of states and a fixed, constant tape alphabet, you need to code $Q$ and&nbsp;$\Gamma$ as multiple symbols in the universal machine's tape alphabet: specifically, you need $\log |Q|$ symbols to write down the current state of the simulated machine, and each character of the simulated tape will take $\log |\Gamma|$ symbols on the universal machine's tape.  (The base of the logarithm will depend on how many symbols you use: for example, simulating in binary will give logs to base&nbsp;2.)

Because of this, the logarithmic slowdown is unavoidable, even if you use multiple tapes.  Indeed, if you only use a single tape, it'll be even worse than logarithmic.

However, see Shreesh's answer for a more significant source of logarithmic overhead, which is logarithmic in the running time of the simulated machine, not just the length of its description.