How do you use the Change of Base Formula and a calculator to evaluate the logarithm #log_2 sqrt2#?

1 Answer
Sep 2, 2015

Answer:

Try this:

Explanation:

Let us see the formula:
#log_bx=log_color(red)(c)x/log_color(red)(c)b#
So let us choose a convenient log such as the natural logarithm #ln# (#=log_e#) that can be easily evaluated by our pocket calculator and apply the formula to get:
#log_2sqrt(2)=log_esqrt(2)/log_e2=lnsqrt(2)/ln2=0.5#

Another way (maybe easier) is to consider:
#sqrt(2)=2^(1/2)#
and
#logx^a=alogx#
so you get:
#log_2sqrt(2)=log_2(2)^(1/2)=1/2log_2(2)=1/2xx1=1/2#