$^{139}$La nuclear quadrupole resonance studies of pressurized La$_4$Ni$_3$O$_{10}$
Density-wave (DW) orders are considered as competing orders to unconventional superconductivity and are commonly seen in a variety of superconductors including but not limited to the recently discovered Ruddlesden-Popper-phase nickelates. By utilizing $^{139}$La nuclear quadrupole resonance, we systematically investigate into the nature of DW orders and their evolution under pressure in La$_4$Ni$_3$O$_{10}$. Spin and charge DW orders are found to be intertwined in this material, which is in stark contrast to those in La$_3$Ni$_2$O$_7$. Short-range DW orders are observed near 150 K, well above the development of long-range DW orders at around 139 K. Upon applying a hydrostatic pressure of 2.3 GPa, the transition temperatures of the short-range and long-range orders decrease at rates of 1 K/GPa and 10 K/GPa, respectively. Our results thus affirm that both spin density wave and charge density wave as competing orders with the superconducting state in La$_4$Ni$_3$O$_{10}$, and provide new insights into the interplay between DW orders and unconventional superconductivity.