Question

Let $N=\left(\log _8 64 \cdot \log _{11} 121 \cdot \log _{10} 100 \cdot \log _{12} 144\right)^2$ then which of the following is/are also equal to $N$ ?
I. $\log _8\left(8^{256}\right)$
II. $\log _4\left(2^{512}\right)$
III. $\log _{16}(256)^8$

• A. I (but not II and III)
• B. I and II (but not III)
• C. II (but not I and III)
• D. I, II and III

Answer 1

Answer: (B)

$N =(2 \times 2 \times 2 \times 2)^2=\left(2^4\right)^2=2^8=256$
$\log _8\left(8^{256}\right)=256 ; \quad \log _4\left(2^{512}\right)=\frac{512}{2}=256 ; \log _{16}(256)^8=\log _{16}(16)^{16}=16$