We use observations of six 'blazars' with the Very Long Baseline Array (VLBA), at eight frequencies (4.6, 5.1, 7.9, 8.9, 12.9, 15.4, 22.2 and 43.1 GHz), to investigate the frequency-dependent position of their VLBI cores ('core-shift') and their overall jet spectral distribution. By cross-correlating the optically thin jet emission, we are able to accurately align the multifrequency images of three of the jets (1418+546, 2007+777, 2200+420), whose core-shifts and spectra we find consistent with the equipartition regime of the Blandford & Konigl conical jet model, where the position of the radio core from the base of the jet follows r(core)(nu) proportional to nu-1. For the jet of 0954+658, we align the higher frequency images using our lower frequency measurements assuming equipartition in the radio core from 4.6-43 GHz. The jet emission of the other two sources in our sample (1156+295, 1749+096) is too sparse for our alignment technique to work. Using our measured core-shifts, we calculate equipartition magnetic field strengths of the order of 10s to 100s of mG in the radio cores of these four AGN from 4.6-43 GHz. Extrapolating our results back to the accretion disc and black hole jet-launching distances, we find magnetic field strengths consistent with those expected from theoretical models of magnetically powered jets.