Calculating PCR Cycles
With every round of PCR, your sample doubles (ideally) and you are right when using $2^n$ for calculating the amount of DNA produced.

The formula would basically be like this:

$$X_{n} = X_0 2^n \\[1em] n=\log_2(X_n/X_0)$$

Just substitute the values of $X_0$ and $X_n$ — 10ng and 1000ng. The answer would be ~6.64 cycles. 

The 500ng case is easier to imagine. The amount is doubled between 1µg and 500ng. So it is just one cycle of PCR.

If this was your answer then you are right. If book says otherwise then it is wrong or you could have read the question wrong.