JEE Advanced 2018 · Paper 1 · Mathematics Q7

MathematicsNumerical+3Question 43 of 54

The value of

$\left((\log_2 9)^2\right)^{\frac{1}{\log_2(\log_2 9)}} \times (\sqrt{7})^{\frac{1}{\log_4 7}}$

is ______ .

Your answer

Answer and worked solution

Official answer: 8

First factor. Use $a^{1/\log_2a}=2$ with $a=\log_29$ :
$\left((\log_29)^2\right)^{\frac1{\log_2(\log_29)}}=\left(a^{1/\log_2a}\right)^2=2^2=4.$

Second factor.
$(\sqrt7)^{\frac1{\log_47}}=7^{\frac12\log_74}=4^{1/2}=2.$

Product: $4\times2=8$ .

Answer: 8

Topics:Logarithms

JEE Advanced 2018 · Paper 1, Mathematics question 7