How do you evaluate #log_4(1/4)#?

1 Answer
Dec 29, 2015

#-1#

Explanation:

The logarithm of the p-th power of a number is p times the logarithm of the number itself:

#color(white)xxlog_4 (1/4)=log_4 (4^-1)#
#color(white)(xxxxxxxx)=color(red)(-1)xxlog_4 4#
#color(white)(xxxxxxxx)=-1#

graph{logx/log4 [-10, 10, -5, 5]}
Graph of #log_4 x#