How do you solve for x?: #2log_3(x) = 3 log_3(4)#

1 Answer
Oct 22, 2015

Answer:

I found #x=8#

Explanation:

We can use a rule of the log to write:
#log_3(x^color(red)(2))=log_3(4^color(red)(3))#

then take #3# to the power of the right and left side to cancel the logs:
#color(blue)(3)^(log_3(x^color(red)(2)))=color(blue)(3)^(log_3(4^color(red)(3)))#
#cancel(color(blue)(3))^(cancel(log_3)(x^color(red)(2)))=cancel(color(blue)(3))^(cancel(log_3)(4^color(red)(3)))#
and get:
#x^2=4^3=64#
#x=+-sqrt(64)=+-8#
we can use only the positive one #x=8#.