How do you use log tables to find logarithm and the antilogarithm of #445.66# ?

1 Answer
May 25, 2017

Answer:

#log 445.66 ~~ 2.6490#

#10^445.66 ~~ 4.571 xx 10^445#

Explanation:

#color(white)()#
Log of #445.66#

In the log table, find the row for numbers beginning #44# and examine the columns for #5# and #6#.

They will contain numbers like #6484# and #6493# respectively.

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Then since #445.66# is about #2/3# of the way between #445# and #446#, we add #(6493-6484)*2/3 = 6# to #6484# to get #6490#

Hence the logarithm of #4.4566# is approximately #0.6490#

Then:

#log(445.66) = log(100*4.4566)#

#= log(100)+log(4.4566) ~~ 2+0.6490 = 2.6490#

#color(white)()#
Antilog of #445.66#

In the antilog table against #0.66# in the #0# column, we find something like #4571#

That tells us that #10^0.66 ~~ 4.571#

Hence:

#10^445.66 ~~ 4.571 xx 10^445#