Home
Class 12
MATHS
The value of ((log(2)9)^(2))^(1/(log(2)...

The value of` ((log_(2)9)^(2))^(1/(log_(2)(log_(2)9)))xx(sqrt7)^(1/(log_(4)7))` is ________.

Text Solution

Verified by Experts

The correct Answer is:
8
`((log_(2)9)^(2))^((1)/(log_(2)(log_(2)9)))xx(sqrt(7))^((1)/(log_(4)7))`
`=(log_(2)9)^(2log(log_(2)9)^(2))xx7^((1)/(2)*log_(7)4) " "[because (1)/(log_(a)b)=log_(b)a]`
`=(log_(2)9)^(2log(log_(2)9)^(2^(2))xx7log_(7)2 " "[because ""_(a)log_(a)b=b]`
`=2^(2) xx 2=8`
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the value of (4/(log_(2)(2sqrt3))+2/(log_(3) (2sqrt3)))^(2) .

Find the value of 3^(2log_(9)3) .

Find the value of log_(5) log_(2)log_(3) log_(2) 512 .

The value of log_(sqrt2)512 is …..

Find the value of sqrt((log_(0.5)4)^(2)) .

Find the value of log_(2) (1/(7^(log_(7) 0.125))) .

Find the value of (1/(49))^(1+(log)_7 2)+5^(-1(log)_((1/5))(7))

The value of log_(9)27 is ………………… .