Answer by Geremia for What is the Merkle root?

"Figure 7-2. Calculating the nodes in a merkle tree" from Mastering Bitcoin shows the Merkle Root (H_ABCD) of a list of four transactions: Tx A, Tx B, Tx C, and Tx D:

---

To verify that a transaction—for example, that with hash H_K—is a valid transaction (i.e., part of a list of, in this example, 16 transactions with hashes H_A, H_B, … H_P), one need only perform at most 2*log₂(N) < N hashes, shown in the Merkle path here:

If H_K leads to the correct Merkle root, then T_K was in the transaction list.

And the Merkle path, needed to verify H_k corresponds with the Merkle root, only contains 4 hashes in the above example. The Merkle path takes up much less space than storing all the transactions in a block. (In the example above: 4 hashes takes much less space than 16.) This is why SPV is lighter-weight.

In this case N = 16, and 2*log₂(16) = 5.55… is indeed less than 16.