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A geometric sequence begins....

 

8,16,32,64...

 

Let x be the 53rd term. What is log_4(x)? 

 May 14, 2022
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common ratio = (second term)/(first term) = 16/8 = 2.

 

That means the 53rd term is \(8 \times 2^{53 - 1} = 8\times 2^{52} = 2^{55}\).

 

We take log_4 of it and get \(\log_4 (x) = \log_4 (2^{55}) = 55 \log_4 (2) = \dfrac{55}2\).

 May 14, 2022

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