How do you solve #log_2 [2^(-13)]#?

2 Answers
ali ergin
Mar 24, 2016

#log_2 2^-13=-13#

Explanation:

#log_2 2^-13=-13*log_2 2#
#log_2 2=1#
#log_2 2^-13=-13*1#
#log_2 2^-13=-13#

Alan P.
Mar 24, 2016

#log_2[2^-13] = -13#

Explanation:

It is important to remember that:
#color(white)("XXX")color(red)(log_b a = c color(white)("XX") "means" color(white)("XX")b^c=a)#

If
#color(white)("XXX")color(blue)(log_2[2^(-13)]=c)#
then we are asking for what value of #color(blue)(c)# is
#color(white)("XXX")color(blue)(2^c = 2^(-13))#

Hopefully the answer is clear that
#color(white)("XXX")color(blue)(c=-13)#

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