I tried to manage using the below command. This will write the output in log file as well as print on console.
#!/bin/bash
# Log Location on Server.
LOG_LOCATION=/home/user/scripts/logs
exec > >(tee -i $LOG_LOCATION/MylogFile.log)
exec 2>&1
echo "Log Location should be: [ $LOG_LOCATION ]"
Please note: This is bash code so if you run it using sh it will through syntax error