Sequence And Series Question 615
Question: The value of $ {a^{{\log_{b}}x}} $ , where $ a=0.2,\ b=\sqrt{5},\ x=\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+……… $ to $ \infty $ is
Options:
A) 1
B) 2
C) $ \frac{1}{2} $
D) 4
Show Answer
Answer:
Correct Answer: D
Solution:
$ x=\frac{1/4}{1-(1/2)}=\frac{1}{2} $
$ \therefore $ $ {{( \frac{1}{5} )}^{{\log_{\sqrt{5}}}( \frac{1}{2} )}}={{( \frac{1}{5} )}^{{\log_5}( \frac{1}{4} )}}={5^{-{\log_5}{4^{-1}}}}={5^{{\log_5}4}}=4 $ .
BETA
