If log_x y = 100 and log₂ x = 10, then the value of y is:

$$\eqalign{ & {\log _2}x = 10\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,x = {2^{10}} \cr & \therefore {\log _x}y = 100 \cr & \Rightarrow y = {x^{100}} \cr & \Rightarrow y = {\left( {{2^{10}}} \right)^{100}}\,\,\,\left[ {{\text{put}}\,{\text{value}}\,{\text{of}}\,x} \right] \cr & \Rightarrow y = {2^{1000}} \cr} $$