Three near 1 fractions applied to log(5)

We will pass from two fractions to three fraction. Let's start with:

5   =   (3/2)^4  *  (81/80)^(-1)

 Fraction  3/2  is not impressive. A modest step toward greater efficiency (of computing log(5)) can be:

3/2  =  (5/4) * (6/5)

Also,

5/4  =  (6/5) * (25/24)

hence

3/2  =  (6/5)^2 * (25/24)

and

5   =   (6/5)^8 * (25/24)^4 * (81/80)^(-1)


Isn't this pretty good? -- maybe. The next note will present a better result, it will do so for all there integers 2 3 5 simultaneously.

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