Ultrafast Laplace NMR (UF-LNMR) reduces the experiment time of multidimensional relaxation and diffusion measurements to a fraction. Here, we demonstrate a method for nonlinear (in this case logarithmic) sampling of the indirect dimension in UF-LNMR measurements. The method is based on the use of frequency-swept pulses with the frequency nonlinearly increasing with time. This leads to an optimized detection of exponential experimental data and significantly improved resolution of LNMR parameters.