Question
If logx y = 100 and log2 x = 10, then the value of y is:
Answer: Option C
$$\eqalign{
& {\log _2}x = 10\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,x = {2^{10}} \cr
& \therefore {\log _x}y = 100 \cr
& \Rightarrow y = {x^{100}} \cr
& \Rightarrow y = {\left( {{2^{10}}} \right)^{100}}\,\,\,\left[ {{\text{put}}\,{\text{value}}\,{\text{of}}\,x} \right] \cr
& \Rightarrow y = {2^{1000}} \cr} $$
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$$\eqalign{
& {\log _2}x = 10\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,x = {2^{10}} \cr
& \therefore {\log _x}y = 100 \cr
& \Rightarrow y = {x^{100}} \cr
& \Rightarrow y = {\left( {{2^{10}}} \right)^{100}}\,\,\,\left[ {{\text{put}}\,{\text{value}}\,{\text{of}}\,x} \right] \cr
& \Rightarrow y = {2^{1000}} \cr} $$
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