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The command "show vtp statistics" is essential for monitoring changes in VLANs because it provides an overview of the VLAN Trunking Protocol (VTP), which is responsible for managing VLAN configurations across a network. This command displays vital information about VTP such as the current VTP state, the number of VLANs configured, and the number of VLANs that have been added or removed. By understanding the VTP statistics, network administrators can track and analyze how VLANs are being propagated across switches in the network, thus enabling effective monitoring of any changes or inconsistencies in VLAN configurations.

While other commands may provide useful information, they do not focus specifically on VLAN changes in the context of VTP. For example, "show vlan brief" lists the VLANs configured on the switch but does not provide information about changes over time or the VTP process itself. "Show interfaces" presents details about interface statuses and configurations rather than VLANs specifically. "Show logging" offers a view of system messages and logs, which may include VLAN-related events but lacks the detailed insights specifically related to VTP and VLAN management.