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Basic of Logarithms
medium
The greatest number among $\root 3 \of 9 ,\root 4 \of {11} ,\root 6 \of {17} $ is
A
$\root 3 \of 9 $
B
$\root 4 \of {11} $
C
$\root 6 \of {17} $
D
Can not be determined
Solution
(a) $\root 3 \of 9 ,\,\,\root 4 \of {11} ,\,\,\root 6 \of {17} $
$L.C.M.$ of $3, 4, 6$ is $12$
$\therefore \sqrt[3]{9} = {9^{1/3}} = {({9^4})^{1/12}} = {(6561)^{1/12}}$
$\root 4 \of {11} = {(11)^{1/4}}{({11^3})^{1/12}} = {(1331)^{1/12}}$,
$\root 6 \of {17} = {(17)^{1/6}} = {({17^2})^{1/2}} = {(289)^{1/12}}$
Hence, $\root 3 \of 9 $ is the greatest number.
Standard 11
Mathematics
