What is #2log_3##9#?

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Answer 1 · 2015-12-18T16:44:30

#=4 #

#2log_3(9)#

As per property of logarithms:
#color(blue)(log_a(a)^b=b#

Applying the same:

#2log_3(9)=2log_3(3)^2#

#=2 * color(blue)(2 #

#=4 #

Answer 2 · 2015-12-18T17:06:08

#y=4#

Solved by comparison.

Given: #2Log_3(9)# and asked to find its value

Let the value be #y# then we have:

#2log_3(9) = y#

#=> log_3(9)=y/2#

#=>3^(y/2)=9........(1)#

but # 9 ->3^2...(2)#

Substitute (2) in (1) giving:

#3^(color(red)(y/2))=3^(color(red)(2))#

From considering the indices we deduce that:

#color(red)(y/2=2)#

#y=4#