48.1. Let the decimal representations of the numbers $2^{1985}$ and $2^{1986}$ contain $p$ and $q$ digits, respectively. Find the sum $p+q$.
48.1. Let:

$$
a=2^{1985}, \quad b=5^{1985} \text {. }
$$

## Then

$$
p-1<\lg a<p, \quad q-1<\lg b<q .
$$

By adding these two inequalities and considering that $\lg (a b)=$ $=1985$, we get:

$$
p+q-2<1985<p+q, \text { hence } \quad 1985<p+q<1987
$$

Therefore, $p+q=1986$.