The value of \(\left(\left(\log _{2} 9\right)^{2}\right)^{\frac{1}{\log _{2}\left(\log _{2} 9\right)}} \times(\sqrt{7})^{\frac{1}{\log _{4} 7}}\) is ____.

JEE Advanced · 2018 · 20 May 2018 · Paper 1 · Basic Mathematics

The value of

((lo g_{2} 9)^{2})^{\frac{1}{l o g _{2} ( l o g _{2} 9 )}} \times (7)^{\frac{1}{l o g _{4} 7}}

is ____.

Answer: 8

Let

t = lo g_{2} 9

. Then the first term is

t^{\frac{2}{l o g _{2} t}} = t^{2 l o g_{t} 2} = t^{l o g_{t} 4} = 4

.

For the second term:

(7)^{\frac{1}{l o g _{4} 7}} = 7^{\frac{1}{2 l o g _{4} 7}} = 7^{\frac{1}{2} l o g_{7} 4} = 7^{l o g_{7} 2} = 2

.

Therefore, the value is

4 \times 2 = 8

JEE Advanced · 2018 · 20 May 2018 · Paper 1 · Numerical answer