Just for fun, let’s calculate all logarithms from scratch.

And let’s start with the logarithm of 2.

I start with doubling 2 a couple of times:

2

4

8

16

32

64

128

256

512

1024

Now, 1024 is a number we can easily guess the logarithm from => a little over 3.

In other words,

(2^{10} = 1024) =>

(log(2^{10}) = log(1024) ) =>

(10*log(2) = log(1024) = 3 + log(1.024) ) =>

(log(2) = 0.3 + log(1.024)/10 )

So the difficult part now is log(1.024).

Let’s use :

Using the triangle, we find that (1.1^7 = 1.9487171), which is almost 2.

Then (1.01^{70}) is also around 2.

let’s use 2.

If 70 times leads to 0.3, then one time is 0.0043.

Otherwise stated:

(1.01^{70} \approx 2 )=>

(log(1.01^{70}) \approx log(2) \approx 0.3 ) =>

(70 * log(1.01) \approx 0.3 ) =>

(log(1.01) \approx 0.3/70 \approx 0.0043 )

(2.4*0.0043) is a little over (0.01).

(we can do this because (1.01 ^{2.4} \approx 1.024) )

Long story short; (log(1.024) \approx 0.01 )

Now we can calculate:

(log(2) = 0.3 + log(1.024)/10 \approx 0.3 + 0.001 = 0.301)