How do you evaluate #log 894.3#?

1 Answer
Mar 19, 2017

Answer:

#log 894.3 ~~ 2.95148323#

Explanation:

Suppose you know:

#log 3 ~~ 0.47712125472#

#ln 10 ~~ 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#