How do you evaluate log_( 1/4)16?

1 Answer
Alan P.
Jul 1, 2016

log_(1/4)16=color(blue)(-2)

Explanation:

Remember that log_b a = c means b^c=a
and that b^c=(1/b)^(-c) (provided c!=0)

If log_(1/4) 16 =c
then
color(white)("XXX")(1/4)^c=16

rArrcolor(white)("XXX")4^(-c)=16

rArrcolor(white)("XXX")-c=2

rArrcolor(white)("XXX")c=-2

Therefore
color(white)("XXX")log_(1/4) 16= -2

Related questions
See all questions in Common Logs
Impact of this question
10025 views around the world
You can reuse this answer
Creative Commons License