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Let me try to answer your questions ... first of all, cardio doesn't necessarily burn muscle. What you've probably read is that TOO MUCH cardio will start to burn muscle when you run out of other fuel for energy. Your body will turn to muscle as an energy source when there isn't anything else left to power your workout. There isn't any specific time when this happens, but most experts agree that more than 60 minutes per cardio session starts to be risky (and is unnecessary for weight loss benefits).
If your cardio workouts are an hour or less, I don't think you're in danger of losing any muscle.
Second, muscle soreness doesn't have anything to do with whether you're building or losing muscle. You can't judge a workout by whether or not you're sore the next day -- the soreness has more to do with a lactic acid build-up than how much you've stressed your muscles.
Third, cardio - like riding your exercise bike - isn't muscle-building exercise. It's great for calorie burning, strengthening, and endurance, but won't build you any new muscle. In order to build muscle, you have to work with weights in order to stress your muscle fibers and build new muscle tissue.
Good for you for recognizing the importance of maintaining your muscle mass! Preserving and increasing your muscle will keep your metabolism running high and make you look tight and toned when you reach goal.
The best way to keep and build muscle is to start a full-body weight training program, not just for your arms. You'll want to do exercises with weights for all
your muscle groups - biceps and triceps (fronts and backs of your arms), shoulders, back, chest, legs, and abs.
The amount of weight to use is going to vary from exercise to exercise and from muscle group to muscle group. The best way to figure out what the right weight is for YOU is to do a set with a certain weight, like your 5# dumbbells. If you can do 12- 15 reps and it's getting really tough or impossible to do any more, then it's the right weight for you. If you get to 15 reps and can keep going, the weight is too light for you and you need to go heavier. If you can't even make it to 12 reps, the weight is too heavy and you need to go ligher. Keep in mind that you'll need to continually adjust your weights as you progress and get stronger.
Protein is the building block of muscle building and repair, so be sure to get enough protein in your diet to support your muscle building workouts! Keep up your cardio, add some more weights, be sure your nutrition is good and you'll do fantastically!!
Hope this helps!