If you want to cheaply see how a log periodic will work, turn a UHF/VHF TV antenna vertically. If its one of the cheaper ones, this would only require drilling two holes in the boom (offset them if possible to retain boom strength). All but the most current TV antennas usually cover the 54 to 870 Mhz range. Very new designs might only cover 174-700 Mhz. It might be possible to pick up a couple used ones from peoples houses who no longer use them.
I picked up an old Channel Master Quantum with the extended UHF section. Since its a dual boom log periodic, its going to require welding a horizontal mast with a counter-weight, and also require replacing 3 of the low band elements that have broken off. Im going to extend the last two elements to 30 Mhz to cover the low band. I am waiting until spring to do it since its going to require some nice weather. Hopefully, it will outperform the expensive "scanner" log periodics that cost several hundred dollars when I am finished.