Based on a sample of (225.3pm2.8)times 10^{6} J/psi events collected with the BESIII detector, the electromagnetic Dalitz decays of J/psi to P e^+e^-(P=eta/eta/pi^0) are studied. By reconstructing the pseudoscalar mesons in various decay modes, the decays J/psi to eta e^+e^-, J/psi to eta e^+e^- and J/psi to pi^0 e^+e^- are observed for the first time. The branching fractions are determined to be mathcal{B}(J/psito eta e^+e^-) = (5.81pm0.16pm0.31)times10^{-5}, mathcal{B}(J/psito eta e^+e^-) = (1.16pm0.07pm0.06)times10^{-5}, and mathcal{B}(J/psito pi^0 e^+e^-)=(7.56pm1.32pm0.50)times10^{-7}, where the first errors are statistical and the second ones systematic.
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