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A geometric sequece begins...

8,16,32,64...

 

Let x be 53rd term in this sequence. Compute $\log_{2}(x)$

 

Pls solve I am confused!!! Thank you!

 May 11, 2022
 #1
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log_2(x) = 58.

 May 11, 2022
 #2
avatar+1768 
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We can rewrite the geometric series as: \(2^3, 2^4, 2^5, 2^6, ...\), where the power is the nth term + 2.

 

This means that x = \(x = 2^ {53+2} = 2^{55}\)

 

Thus, we have \(\log_2(2^{55})\)

 

This is the same as: \(2^y = 2^{55}\), where y is our final answer. Can you take it from here?

 May 11, 2022
 #3
avatar+27 
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Yes thank you!

 May 12, 2022

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