Binomial-Theorem-And-Its-Simple-Applications Question 216
Question: If the third term in the expansion of $ {{[x+{x^{{\log_{,10}},x}}]}^{5}} $ is $ 10^{6} $ , then x may be
Options:
A) 1
B) $ \sqrt{10} $
C) 10
D) $ {10^{-2/5}} $
Correct Answer: C
Show Answer
Answer:
Solution:
$ \Rightarrow (3+2y)log_{10}x=5,{\log_{10}}10=5 $
$ \Rightarrow (3+2y)y=5 $
$ \Rightarrow y=1,-\frac{5}{2}\Rightarrow {\log_{10}}x=1 $ or $ {\log_{10}}x=-\frac{5}{2} $
$ \therefore ,x=10 $ or $ x={{(10)}^{-5/2}} $
BETA
