Question

A geometric sequence begins 8,16,32,64.... let x be the 53rd term in this sequence. compute log_2(x)

Answer 1

These are sequence that increases in an exponential manner. The value of the log function is 55

Geometric sequence

These are sequence that increases in an exponential manner. The nth term of the sequence is expressed as:

Tn = ar^n-1

Given the following

• first term a = 8
• common ratio "r" = 16/8 = 2
• number of terms n = 53

Substitute

Tn = x = 8(2)^52
x = 8(2)^52

Take the log of the result to have:

$log_28(2)^{52} = log_22^{55}\\ log_22^{55} = 55log_22=55$

Hence the value of the log function is 55

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