A) 4200
B) 5100
C) 2250
D) 2150
Correct Answer: A
Solution :
(a): Comparing between \[{{\mathbf{2}}^{\mathbf{250}}},{{\mathbf{3}}^{\mathbf{150}}},{{\mathbf{4}}^{\mathbf{200}}},\] the obvious result (for largest) is 4200 . Now between 5100 & 4200. Taking log, 100 log 5 and 200 log4 have to be compared Let us write 200 as \[100\times 2.\] \[\therefore 200\,\text{log}\,4=100\times 2\text{ }log\text{ }4\] \[=100\times \text{log}\,{{4}^{2}}\] \[=100\times \text{log}\,16\] Now comparing 100 log 5 and 100 \[\times \] log 16, latter is obviously greater \[\Rightarrow \]100 log 16 = 200 log 4 \[\Rightarrow \]\[{{4}^{200}}\] is the greatest.
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