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Real Values Satisfaction (Posted on 2024-10-01)

Determine all possible real values of n that satisfy this equation:

           nⁿ = 81√6/32.

No Solution Yet Submitted by K Sengupta

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Solution

Comment 7 of 7 |

Every number on the right hand side consists solely of prime factors of 2 and 3. So rewrite the expression accordingly and simplify:

81*sqrt[6]/32

= 3^4 * 2*(1/2) * 3^(1/2) * 2^(-5)

= 3^(9/2) * 2*(-9/2)

= (3/2)^(9/2)

= ((3/2)^2)^((9/2)*(1/2))

= (9/4)^(9/4)

n=9/4

Posted by Brian Smith on 2024-10-02 11:28:51

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