  We present 3 mm and 2 mm band simultaneously spectroscopic observations of
HCN 1-0, HCO$^{+}$ 1-0, HNC 1-0, and CS 3-2 with the IRAM 30 meter telescope,
toward a sample of 70 sources as nearby galaxies with infrared luminosities
ranging from several 10$^{5}L_{\odot}$ to more than 10$^{12}L_{\odot}$. After
combining HCN 1-0, HCO$^{+}$ 1-0 and HNC 1-0 data from literature with our
detections, relations between luminosities of dense gas tracers (HCN 1-0,
HCO$^{+}$ 1-0 and HNC 1-0) and infrared luminosities are derived, with tight
linear correlations for all tracers. Luminosities of CS 3-2 with only our
observations also show tight linear correlation with infrared luminosities. No
systematic difference is found for tracing dense molecular gas among these
tracers. Star formation efficiencies for dense gas with different tracers also
do not show any trend along different infrared luminosities. Our study also
shows that HCN/HCO$^{+}$ line ratio might not be a good indicator to diagnose
obscured AGN in galaxies.
