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Find the Value of X in the Following: `(13)^(Sqrtx)=4^4-3^4-6` - CBSE Class 9 - Mathematics

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Question

Find the value of x in the following:

`(13)^(sqrtx)=4^4-3^4-6`

Solution

Given `(13)^(sqrtx)=4^4-3^4-6`

`(13)^(sqrtx)=(2^2)^4-3^4-6`

`rArr(13)^(sqrtx)=2^8-3^4-6`

`rArr(13)^sqrtx=256-81-6`

`rArr(13)^sqrtx=169`

`rArr(13)^sqrtx=(13)^2`

On comparing we get,

`sqrtx=2`

On squaring both side we get,

x = 4

Hence, the value of x = 4.

  Is there an error in this question or solution?

APPEARS IN

 RD Sharma Solution for Mathematics for Class 9 by R D Sharma (2018-19 Session) (2018 to Current)
Chapter 2: Exponents of Real Numbers
Ex. 2.20 | Q: 10.8 | Page no. 26

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Solution Find the Value of X in the Following: `(13)^(Sqrtx)=4^4-3^4-6` Concept: Laws of Exponents for Real Numbers.
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