Answers to 2 past answers: logarithm
=LOG(10^9;2)
=30 steps
what I write at once: numbers are cyclopean
and number of steps is logarithmic
Logarithm: those who understand think faster
My express lecture over 5 years ago from 2010++ years about...
Logarithm of Life
annually something changes in multiple
? through what QUANTITY of years is
something will give growth in right scale ?
SCALE is: GROWTH to extent of QUANTITY
SCALE = GROWTH ^ QUANTITY
QUANTITY: to what extent do you build
GROWTH to get SCALE
LOGARIFM: to what extent to erect
GROWTH to get SCALE
excel formula: QUANTITY = ...
=LOG(SCALE;GROWTH)
check: something annually grows 2 times
? in how many years
something will grow 64 times ?
SCALE = GROWTH ^ YEARS
64 = 2 ^ YEARS
YEAR = LOG(SCALE;GROWTH)
= LOG(64;2)
= 6
answer: over 6 years
example: over 25 years of inflation
devalued money 12 times
? what was inflation every year ?
? what was logarithm of inflation ?
? what should be growth to something
would have grown 12 times over 25 years ?
YEAR = LOG (SCALE;GROWTH)
GROWTH = SCALE ^ (1 / YEARS)
GROWTH = 12 ^ (1/25)
GROWTH = 1.1045 = 10.5 % per year
translate to same logarithm:
decimal: = LOG (SCALE) / LOG (GROWTH)
natural: = LN (SCALE) / LN (GROWTH)