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

Find the value of x in the following:

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

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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.

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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 2 Exponents of Real Numbers
Exercise 2.2 | Q 10.8 | Page 26
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