Thanks to some info from Rob PE9PE, I came across this commercial antenna website in the USA ... https://antennaproducts.com/
Part of their wide range of products includes log-periodic directional antennas for the low VHF band of about 30 to 80 MHz.
The general principle of a log-periodic antenna is that they give a modest amount of gain over a very wide bandwidth as opposed to a typical Yagi which has more gain but only a narrower bandwidth.
While these commercial products are perhaps outside the budget of the typical radio amateur or scanner enthusiast, they do give some idea on the performance to expect from this type of antenna.
Model : TLP-20 (pictured above)
Range : 20 MHz - 1000 MHz
Boom Length : 5.1m
Gain : Approx 2 to 6dBd
Link : https://antennaproducts.com/wp-content/uploads/2014/09/TLP-20-1.pdf
Model : LP-102
Range : 30 MHz - 88 MHz
Boom Length : 4.5m
Gain : Approx 5.4 dBd
Link : https://antennaproducts.com/wp-content/uploads/2014/04/LP-102.pdf
Model : TLP-28
Range : 28 MHz - 100 MHz
Boom Length : 4.1m
Gain : Approx 3dBd
Link : https://antennaproducts.com/wp-content/uploads/2014/04/TLP-28100225.pdf
The website of the company is https://antennaproducts.com/