How do you simplify #log_3 27 + 6log_3 9#?

1 Answer
Mar 27, 2016

Answer:

#log_3 27 + 6 log_3 9 = color(green)(15)#

Explanation:

Always remember when dealing with log functions
#color(white)("XXX")log_b a = c hArr b^c=a#

So
#color(white)("XXX")color(red)(log_3 27= c_1)#
#color(white)("XXXXXX")#means #3^(c_1)=27 rarr color(red)(c_1=3)#
and
#color(white)("XXX")color(blue)(log_3 9 = c_2)#
#color(white)("XXXXXX")#means #3^(c_2) = 9 rarr color(blue)(c_2=2)#

Therefore
#color(white)("XXX")color(red)(log_3 27) + 6 color(blue)(log_3 9)#
#color(white)("XXX")=color(red)(3)+6*color(blue)(2)#
#color(white)("XXX")=15#