With a PIC it is a little difficult to do all the math and stil have time for the A/D and display.

Also for the Log function you might need floating point calculations (even slower...).

If 55-60db dynamics are enough for you with linear response then you have to:

1. amplify the signal to be in the range of 0-5 volt
2. use an absoluter value converter to feed the A/D of the PIC with just positive voltages
3. setup PIC to continusly read the analog value, make a small average and display it

If you insist on making it logarithmic then use an CA3089 or CA3189 chip and take advantage of the log amplifier that is used for the AGC and S-meter.

And if you want to do the math way, have a look at http://www.emesys.com/BS2math3.htm#Logtable

Ioannis