Here is how to calculate the antilogarithm of 0.87 (the easiest way).

Recall:

log 7 = 0.845

log 8 = 3 X log 2 = 3 X 0.301 = 0.903.

So .87 can be found between 7 and 8 and probably close the the middle.

The average of the two is:

(0.845 + 0.903)/2 = 1.748/2 = 0.874

To find the middle of 7 and 8 in terms of antilogs we need to find the so called geometric mean.

7 times 8 = 56 and the geometric mean is the square root of 56.

Now 7.5 X 7.5 = 56.25.

56.25 is about half a percent too big (it is actually a little smaller than a half percent).

So the square root of 56 is about half that half percent smaller than 7.5. This is a quarter percent of course.

So a guess of 7,48 is in order.

But now we have the antilog of 0.874. And we need 0.87!

A drop of 0.004 is about 1%, as you have learned from the video, so subtract 7 cents from 7.48 and get 7.41.

So the antilog of 0.87 is 7.41.