4. Let $2^{a}=3, 2^{b}=6, 2^{c}=12$. Given the following four relationships among the real numbers $a, b, c$:
(1) $a+c=2b$,
(2) $a+b=2c-3$,
(3) $b+c=2a+3$, (4) $b^{2}-ac=1$.
The number of correct relationships is ( ).
(A) 1
(B) 2
(C) 3
(D) 4
4.D.

Notice that $2^{a}=3$,
$$
\begin{array}{l}
2^{b}=6=3 \times 2=2^{a} \times 2=2^{a+1}, \\
2^{c}=12=6 \times 2=2^{b} \times 2=2^{b+1} \\
=3 \times 4=2^{a} \times 2^{2}=2^{a+2} .
\end{array}
$$
$$
\begin{array}{l}
\text { Hence } b=a+1, c=b+1 \\
\Rightarrow a=b-1, c=b+1 \\
\Rightarrow a+c=2 b, b^{2}-a c=1 .
\end{array}
$$

From $c=b+1, c=a+2 \Rightarrow a+b=2 c-3$.
From $b=a+1, c=a+2 \Rightarrow b+c=2 a+3$.