Richard,

I don't know which log periodic you had in mind, but for the fun of it, I
found a log periodic on m2inc.com(M Square) coving 13 MHz thru 30 MHz.
Reading the specs on this log periodic, and assuming that it is similar to
other logs covering the same frequency range, a telescoping mast may not be
anywhere near sufficient to hold the antenna, see the antennas specs below.
It is model 13-30lp11.  .  This example that fits your stated frequency
range weighs approximately 73 pounds, and has a wind load of 10.5 square
feet.  In addition to the weight and wind load of the antenna, you have to
take into account the weight of the rotor and feed line(s), and possibly
hardware, etc.

SPECIFICATIONS:
Model
13-30LP11
Frequency Range
13.0-30.0 MHz
Gain
6.8 dBi / 11.6 dBi @ 45'
Front to Back
20 dB Typical
Usable Range
13.0-30.0 MHz
Beam Width
E=68
Feed Type
4:1 Balun
Feed Impedance
50 Ohms Unbalanced
Max VSWR
1.2:1 Typical
Input Connector
SO-239
Boom Length / Dia
37' / 3" to 2"
Max Element Length / Dia
22' 9"
Turning Radius
27' 6"
Mast Size
2" or 3"
Wind area / Survival
10.5 Sq Ft. / 80 MPH
Weight / Ship Wt
73 lbs. / 85 lbs.
FEATURES:
The 1330LP12 removes the concern many share regarding the complexity and
cost of
other multiband antennas.  This high performance log periodic covers every
frequency,
instantly, from 10 to 30 MHz! Just one feedline is all you need to access
it's flawless
performance.  This antenna is a band opener!
We have done everything possible to keep cost down and performance up!  This
standard
version is built for 80+ mph winds and years and years of no maintenance,
trouble
free performance. For those who need to be small now but are planning big,
we designed
the
1330LP11 so it can morph into it's big brother, the 1030LP12. An optional
kit will
add the rear boom and the 10 MHz element to give you full 10 to 30 MHz
coverage.**Subtract
2.14 from dBi for dBd**(Rev-062111/01)

[*] 
HTH

Alan/KD7GC