first three terms of the arithmetic sequence

Question

The first three terms of the arithmetic sequence (in order) are
log ,base2,x / log ,base2, (x/2) / log ,base2, (x/4), where x > 0

 

How do I find d, giving my answer as an integer?

Answer 1

In what I write below, all logariths bases are two (implied, so I don't go nuts typing subscripts all over the place).

 

The general term can be written as log (x/2ⁿ), and because the log of a quotient is the log of the numerator minus the log of the denominator, that simplifies to log x - n log 2 = log x - n SINCE log₂2 = 1.

 

Those three terms are log x, log x - 1 and log x - 2.

 

Now you see that d = 1, the constant difference.