Given log 2( log 8 x)= log 8( log 2 x) then ( log 2 x)2 has the value equal to

Question

Given log 2( log 8 x)= log 8( log 2 x) then ( log 2 x)2 has the value equal to (A) 9 (B) 12 (C) 27 (D) 3 √3

Tardigrade Admin · Accepted Answer

Given log 2((1/3) log 2 x)=(1/3) log 2( log 2 x) let log 2 x=3 y ⇒ log 2 y =(1/3) log 2 3 y ⇒ 3 log 2 y = log 2 3+ log 2 y ⇒ 2 log 2 y = log 2 3 ⇒ y 2=3 ⇒ (1/9)( log 2 x )2=3 ⇒ ( log 2 x )2=27

Q. Given $lo g_{2} (lo g_{8} x) = lo g_{8} (lo g_{2} x)$ then $(lo g_{2} x)^{2}$ has the value equal to

9

12

27

$33$

Q. Given log2​(log8​x)=log8​(log2​x) then (log2​x)2 has the value equal to

9

12

27

33​

Given log2​(31​log2​x)=31​log2​(log2​x) let log2​x=3y ⇒log2​y=31​log2​3y⇒3log2​y=log2​3+log2​y⇒2log2​y=log2​3 ⇒y2=3⇒91​(log2​x)2=3⇒(log2​x)2=27

Q. Given $lo g_{2} (lo g_{8} x) = lo g_{8} (lo g_{2} x)$ then $(lo g_{2} x)^{2}$ has the value equal to

$33$