How do you evaluate #log_10 sqrt(10)#?

1 Answer
John C.
May 7, 2017

#1/2#

Explanation:

#log_a b^c#
#color(red)a# is the base, #color(blue)b# is the number and #color(orange)c# is the power/exponent.

#log_10 sqrt10#
#=log_10 10^(1/2)#

The properties of a logarithmic function allows the exponent to be "brought" down as such:

#=log_10 10^(1/2)#
#=(1/2)log_10 10#

When the base is equal to the logarithmic number , the result is 1 eg. #(log_2 2 = 1 , log_3 3= 1 , log_1000 1000= 1)#.

#=(1/2)log_10 10#
#=(1/2)# x #1#
#=1/2#

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