How to know the number of bits used to represent a number?

There certainly is. Unfortunately, your answers are not quite correct — the right answers are 7 bits for 82 and 8 for 136.

Think about how many decimal digits it takes to represent a number. For example, 2 for 82 or 3 for 136. In each case it takes as many digits as the next highest power of 10. For 82, the next highest power of 10 is 100, which is 10^2, so you have 2 digits. With 136, the next highest power of 10 is 1000, which is 10^3, so you need 3 digits.

It works exactly the same in binary, except you're looking at powers of 2 instead of powers of 10. With 82, the next highest power of 2 is 128, which is 2^7. Therefore, you need 7 binary digits (bits) to represent 82. For 136, the next highest power of 2 is 256, which is 2^8, so you need 8 bits.