You need to make changes to the configuration of the logging of your ESXi hosts. You want to modify the rotation of the log files, such that the most recent 20 logs are maintained.
VDCA510 Objective: 6.1 Configure, Manage, and Analyze vSphere Log Files
VDCA550 Objective: 5.4 Configure, Manage, and Analyze vSphere and SSO Log Files
esxcli system syslog config get
esxcli system syslog config set –default-rotate=20
esxcli system syslog reload
esxcli system syslog config get