Materials tuned to a quantum critical point display universal scaling properties as a function of temperatureTand frequencyω. A long-standing puzzle regarding cuprate superconductors has been the observed power-law dependence of optical conductivity with an exponent smaller than one, in contrast toT-linear dependence of the resistivity andω-linear dependence of the optical scattering rate. Here, we present and analyze resistivity and optical conductivity of La2−xSrxCuO4withx= 0.24. We demonstrateℏω/kBTscaling of the optical data over a wide range of frequency and temperature,T-linear resistivity, and optical effective mass proportional to\documentclass[12pt]{minimal}
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				\begin{document}$$\sim \ln T$$\end{document}~lnTcorroborating previous specific heat experiments. We show that aT,ω-linear scalingAnsatzfor the inelastic scattering rate leads to a unified theoretical description of the experimental data, including the power-law of the optical conductivity. This theoretical framework provides new opportunities for describing the unique properties of quantum critical matter.