What is the value of the common logarithm log 10,000?

1 Answer
Sep 13, 2014

Logarithms in base 10 (common log) is the power of 10 that produces that number.
log(10,000) = 4 since #10^4=10000#.

Additional examples:
#log(100)=2#
#log(10)=1#
#log(1) = 0#

And:
#log(frac{1}{10})=-1#
#log(.1)=-1#

The domain of the common log as well as the logarithm in any base, is x > 0. You can not take a log of a negative number, since any positive base can NOT produce a negative number, no matter what the power!

Ex: #log_2(8)=3# and #log_2(frac{1}{8})=-3#
#log_3(9)=2# since #3^2=9#

#log_5(-5)# is undefined!