A geometric sequence begins....
8,16,32,64...
Let x be the 53rd term. What is log_4(x)?
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 \(\log_4 (x) = \log_4 (2^{55}) = 55 \log_4 (2) = \dfrac{55}2\).