There are few things you need to be aware off when exercising in ketogenic state.
1. You need to slowly ramp up the exercise when you are switching the body fuel from carbs to fat. Its not going to happen over night. Go with weight training and low intensity cardio (if you really need to do cardio).
2. If you do high intensity, the body can't use fat as fuel, especially in early part of keto adaption when your anaerobic threshold is low. Doing high intensity works outs in anaerobic zone puts lot of pressure on your liver to generate glucose. You have two options, easy one is to increase carbs, the other to slowly build up the intensity with out eating more carbs.
3. You make sure you eat enough and are getting the electrolytes right if you are working out.

I didn't even work out for 4 weeks when I started Keto, I struggled for first few weeks till I adjusted the intensity of workouts. I didn't take more carbs because I wanted my body to completely switch to fats even at higher intensities. After 6 months, now my body switches to carbs at a HR of 173, which is like 92% of Max HR. Slowly build your intensity and remember maximum fat burn happens with resistance/weight training. You are not gaining much with HIIT as your carbs are already lower compared to some one on a HC diet who needs to burn ton of carbs at high intensity.

I just started at the gym last week and other than walking the dogs had done very little exercise before this. I`m working on my strength exercise, using the weight machines & so far I`m finding my muscles are quiet weak. How do you know if you are fully adapted? I've been at this since March 1st and have had a hard time getting ketones up over 1.5.

Endurance work can benefit by having some more carbs, however, note that it will burn more _muscle_ than other forms of exercise -- specifically in the middle-intensity level (i.e. something you can sustain for 30-90 minutes, e.g. jogging, etc.)

Very-low-intensity work (e.g. walking) is a great way to burn some extra fat, because even though it's sustained, it's not as catabolic on breaking down muscle as that middle-intensity stuff. Starting the day with a 30-60 minute walk (especially before eating) is a great way to burn a couple extra hundred calories.

On a keto diet, high-intensity training works quite well for many (using bursts of energy instead of a sustained, low-intensity thing like endurance training). Example would be strength training in sets of 3-10 reps, especially in the magic 3-5 rep range (e.g. using a weight that you can only lift for sets of 3-5 with decent form). This will build strength, burn fat, and help build muscle (although arguably the 8-12 range is optimal for hypertrophy).

Remember: a pound of muscle burns a lot more calories than a pound of fat -- if you have a bigger "engine", you burn more "fuel", which means for a given number of calories, the person with more muscle can have a larger deficit and burn more fat.