13 db correspond to a power ratio of

19.95

Explanation:

Power ratio (in db) = 10 * log [P(out)/P(in)]

Here, P(in) and P(out) correspond to input and output power in Watts respectively.

This implies, 13 db = 10 * log [P(out)/P(in)]

Rearranging,  log [P(out)/P(in)] = (13/10)

Or, P(out)/P(in) = 10 ^ 1.3 = 19.95

But, P(out)/P(in) corresponds to the power ratio of output and input power.

So the required power ratio corresponds to 19.95