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# Geometric sequence

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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