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what is the value of n such that, 81^n=9*27*27*9?

 Jan 8, 2023
 #1
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 81^n=9*27*27*9?

 

n ==Log[9*27*27*9) / log(81)

 

n==2.5

 Jan 8, 2023
 #2
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Alternatively:

 

\(81^n=9^{2n}\)

 

\(9*27*27*9=9*3*9*3*9*9=9^5\)

 

Hence \(9^{2n}=9^5\)  so \(2n=5\)  or \(n=5/2\)

 Jan 8, 2023

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