Let N=( log 8 64 ⋅ log 11 121 ⋅ log 10 100 ⋅ log 12 144)2 then which of the following is/are also equal to N ? I. log 8(8256) II. log 4(2512) III. log 16(256)8

Question

Let N=( log 8 64 ⋅ log 11 121 ⋅ log 10 100 ⋅ log 12 144)2 then which of the following is/are also equal to N ? I. log 8(8256) II. log 4(2512) 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

Tardigrade Admin · Accepted Answer

N =(2 × 2 × 2 × 2)2=(24)2=28=256 log 8(8256)=256 ; log 4(2512)=(512/2)=256 ; log 16(256)8= log 16(16)16=16

Q. Let $N = (lo g_{8} 64 \cdot lo g_{11} 121 \cdot lo g_{10} 100 \cdot lo g_{12} 144)^{2}$ then which of the following is/are also equal to $N$ ?
I. $lo g_{8} (8^{256})$
II. $lo g_{4} (2^{512})$
III. $lo g_{16} (256)^{8}$

I (but not II and III)

I and II (but not III)

II (but not I and III)

I, II and III

$N = (2 \times 2 \times 2 \times 2)^{2} = (2^{4})^{2} = 2^{8} = 256$
$lo g_{8} (8^{256}) = 256; lo g_{4} (2^{512}) = \frac{512}{2} = 256; lo g_{16} (256)^{8} = lo g_{16} (16)^{16} = 16$

Q. Let N=(log8​64⋅log11​121⋅log10​100⋅log12​144)2 then which of the following is/are also equal to N ? I. log8​(8256) II. log4​(2512) III. log16​(256)8