Toda vez que tendo iniciar o serviço dhcp recebo a seguinte mensagem “
dhcpd3check syslog for diagnostics. Failed!”

Verifiquei o syslog
Com a seguinte mensagem abaixo

Wrote 0 lease to lease file
No subnet declaration for eth0 (0.0.0.0).
** Ignoring request on eth0. If this is not what you want, please write a
subnet declaration in your dhcpd.con fle for the network segment to which
interface eth0 is attached. **

Not configured to liten on any interfaces!

Segue a minha configuração abaixo;
Configuração do meu modem DHCP ativo 10.0.0.138 cabo do modem esta conectado
na eth0  e a eth2 na rede

# /etc/dhcp3/dhcpd.conf
ddns-update-style none;
default-lease-time 600;
max-lease-time 7200;
authoritative;
subnet 10.0.0.0 netmask 255.255.0.0 {
range 10.0.0.100 10.0.0.199;
option routers 10.0.0.138;
option domain-name-servers 200.204.0.10,200.204.0.138;
option broadcast-address 10.0.0.255;
}

#/etc/default/dhcp3-server

INTERFACES="eth0"

#/etc/network/interfaces

auto lo
iface lo inet loopback

# Rede Loca
auto eth0
iface eth0 inet dhcp
address 10.0.0.1
netmask 255.255.0.0
gateway 10.0.0.138

# internet

auto eth2
iface eth2 inet static
address 10.0.0.3
netmask 255.255.0.0
gateway 10.0.0.138

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