How do you condense #1/4log_3a+5log_3b-log_3c#?

1 Answer
Bdub
Mar 9, 2017

see below

Explanation:

Use the following Properties of Logarithim:

  1. #log_b x^n =n log_b x#

  2. #log_b (xy)=log_bx+log_by#

  3. #log_b(x/y)=log_bx-log_by#

Hence,

#1/4 log_3 a+5 log_3 b - log_3 c = log_3 a^(1/4)+log_3b^5-log_3 c#

#=log_3 ((a^(1/4) b^5) / c)#

#=log_3 ((root 4 (a) b^5)/c)#

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