How do you evaluate log 894.3log894.3?
1 Answer
Mar 19, 2017
Explanation:
Suppose you know:
log 3 ~~ 0.47712125472log3≈0.47712125472
ln 10 ~~ 2.302585093ln10≈2.302585093
ln (1-x) = -(x/1+x^2/2+x^3/3+...)
We find:
894.3 = 900*(1-19/3000) = 3*3*10*10*(1-19/3000)
Then:
log 894.3 = log (3*3*10*10*(1-19/3000))
color(white)(log 894.3) = log 3 + log 3 + log 10 + log 10 + ln (1-19/3000) / ln 10
color(white)(log 894.3) ~~ 2*0.47712125472 + 2 - (19/3000+19^2/(2*3000^2)+19^3/(3*3000^3)) / 2.302585093
color(white)(log 894.3) ~~ 2.95148323
