How do you condense #1/3log_(2)27 - log_(2)9 #?

1 Answer
May 18, 2016

Answer:

#- log3/log 2=-ln 3/ln 2=-1.585#, nearly.

Explanation:

Use #log_b (m/n)=log_b m - log_b n, nlog_b a =log_b(a^n)# and

#log_b a = log a/log b = ln a/ln b#.

Here, #(1/3)log_2 27-log_2 9=log_2(27^(1/3)) - log_2 9#

#=log_2 3 - log_2 9=log_2(3/9)=log_2(1/3)#

#=-log_2 3=-log 3/log 2=-ln 3/ln 2=-1.585#, nearly