Home
Class 12
MATHS
If 3^(((log3 7))^x)=7^(((log7 3))^x), th...

If `3^(((log_3 7))^x)=7^(((log_7 3))^x)`, then the value of x will be

A

`(1)/(2)`

B

`(1)/(4)`

C

`(1)/(3)`

D

1

Text Solution

Verified by Experts

The correct Answer is:
A
Consider `a^(sqrt(log_(a)b))=b^(sqrt(log_(b)a))`
`therefore sqrt(log_(a)b)= sqrt(log_(b)a) log_(a)b` (taking log with base 'a')
`rarr 1=sqrt(log_(b)a).sqrt(log_(a)b)` which is true
`therefore` from `3^((log_(3)7)^(x))=7^((log_(7)3)^(x)), x=(1)/(2)`
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND ITS APPLICATIONS

    CENGAGE|Exercise Subjective Type|9 Videos

  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE|Exercise DPP 1.2|10 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise JEE Previous Year|5 Videos

Similar Questions

Explore conceptually related problems

If log_(7)x = 4/3 , then the value of x is:

log_(2)x=-log_((1)/(2))7, then the value of x is

If log_(3)27.log_x7=log_(27)x.log_(7)3 , the least value of x is

If log_3 2+log_3 (2^x-7/2)=2log_3 (2^x-5) then x=

If log_(175)5x=log_(343)7x , then the value of log_(42)(x^(4)-2x^(2)+7) is

log_3 2 ,log_3(2^x-5) , log_3(2^x-7/2) are in A.P. then the value of x =?

sqrt(log_(3)7)=x^(sqrt(log_(7)3))find x