<prompt> Acha x na y ziwe nambari halisi kubwa kuliko 1 kama hizolog_2 x4 log_3 y4 8 8 log_2 xlog_3 y.Kokotoa xsqrt2 y sqrt2.  <response>: Acha a log_2 x na b log_3 y. Tangu x 1 na y 1, a 0 na b 0.Na AM-GM,anzaaligna4 b4 8 a4 b4 4 4 ge 4 sqrt4a4b444 8ab.endalignKwa kuwa a4 b4 8 8ab, tuna usawa. Kwa hivyo, a4 4 na b4 4. Kisha a sqrt44 sqrt2, hivyox 2a 2sqrt2.Vile vile, b sqrt44 sqrt2, hivyoy 3b 3sqrt2.Kwa hivyo, xsqrt2 ysqrt2 22 32 13. 