How to mentally calculate log43 and log85?

[Kinma]

85 is 17 * 5, so if you remember both log17 and log5, which we calculated here:

Calculating logarithms by hand

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 [Pascals triangle]: Using the triangl…

then you can just add the two numbers together.