Complex Numbers And Quadratic Equations question 736
Question: The roots of the equation $ {2^{x+2}}{27^{x/(x-1)}}=9 $ are given by
Options:
A) $ 1-{\log_2}3,2 $
B) $ {\log_2}( \frac{2}{3} ),\ 1 $
C) $ 2,-2 $
D) $ -2,\ 1-\frac{\log 3}{\log 2} $
Show Answer
Answer:
Correct Answer: D
Solution:
$ {2^{x+2}}{{.3}^{3x/(x-1)}}=9 $ Taking log, we get $ (x+2)\log 2+( \frac{3x}{x-1} )\log 3=2\log 3 $
Þ $ (x+2)( \log 2+\frac{1}{x-1}\log 3 )=0 $
Þ $ x=-2 $ or $ \frac{1}{1-x}=\frac{\log 2}{\log 3} $
Þ $ 1-x=\frac{\log 3}{\log 2} $
Þ $ x=1-\frac{\log 3}{\log 2} $
BETA
