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