Question

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

Answer 1

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`