Cho a,b, c là các số thực dương a^{log_3}7=27, b^{log_7}11=49, c^{log_11}25=sqrt11

$T = {a^{\log _3^27}} + {b^{\log _7^211}} + {c^{\log _{11}^225}} = {\left( {{a^{{{\log }_3}7}}} \right)^{{{\log }_3}7}} + {\left( {{b^{{{\log }_7}11}}} \right)^{{{\log }_7}11}} + {\left( {{c^{{{\log }_{11}}25}}} \right)^{{{\log }_{11}}25}}$

$= {\left( {27} \right)^{{{\log }_3}7}} + {\left( {49} \right)^{{{\log }_7}11}} + {\left( {\sqrt {11} } \right)^{{{\log }_{11}}25}} = {7^3} + {11^2} + \sqrt {25} = 469.$