How do you evaluate log_10 sqrt(10)?

1 Answer
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