Mental logarithms

Logarithms (log_10(x)) (from World Mental Calculation)

• Choose a number very close to the original number that you can construct using factors whose logarithms you have learnt,

• calculate the logarithm of this approximated number, and

• calculate the percentage error and multiply the value (without the percent) by log(1.01) = 0.00432, and add or subtract as appropriate.

Antilogarithms (10^x) (from World Mental Calculation)

• Using the memorized values for various logarithms, find a number whose logarithm is close to the target number.

• Find the error between the target and this logarithm and if necessary return to the previous step to find a better candidate logarithm.

• When you have selected a sufficiently close logarithm and have calculated its error, compute the correction factor, which is approximately 1% for every 0.00432 in the error.

Some log values to memorize

Essentials
log(2) = 0.30103
log(3) = 0.47712
log(5) = 0.69897 (or you could use -0.30103)
log(7) = 0.84510

Extras
log(1.1) = 0.04139
log(1.3) = 0.11394
log(1.7) = 0.23045
log(1.9) = 0.27875

(optionally more if you would like to)

The special one
log(1.01) = 0.00432

Example solves

Logarithm: -

Antilogarithm: -