approximate the logarithm, using log base b of 2 is = to about 1.098, log base b of 3 is about 1.740, and log base b 5 is about 2.5495?

Recall that the log of a product is the same as the sum of the logs:

log(xy) = log(x) + log(y)

base of b is to be presumed from this point on, so I don't have to write it each time. In fact, I'll make up a new notation for it "lob" (log of base b) :)

You have:

lob(6)

Which is the product of 2 and 3, so:

lob(2 * 3)

Now apply the sum of the logs rule above:

lob(2) + lob(3)

And we know what lob(2) and lob(3) are, so substitute:

1.098 + 1.740 = 2.838

Same with 20 if you think of it as 2 * 2 * 5.

logb 6=logb (2*3)=logb 2+logb 3=1.098+1.740=2.838

logb 20=logb (4*5)=2logb 2+logb 5= 2(1.098)+2.5495= 4.7455

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