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 2x^((log)_4 3)+3^((log)_4x)=27 , then x is equal to

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

If log ((x+y)/3)=1/2 (log x +log y) then find the value of x/y+y/x

If log_2x+log_(4)x+log_(16)x=7/2 , find the value of x.

Given that log_2 3 = a, log_3 5=b,log_7 2=c ,then the value of log_(140) 63 is equal to

Solve x^(log_(4) x)=2^(3(log_(4)x+3) .

If x=7+4sqrt3 then find the value of x+(1)/(x)

If (7,x) (-3,3) (2,2) are collinear then the value of x is: