How do you evaluate #log_3 (1/243)#?

1 Answer
Oct 1, 2016

#log_3 (1/243) = log_3 3^-5 = -5#

Explanation:

Logs and exponential equations become much easier to understand if you know the powers up to 1,00.

Note that #243 = 3^5#

#log_3 (1/243)# is asking the question..

#"What index of 3 gives "1/243#?

#1/243 " is which power of " 3#?

#1/243 = 1/3^5 = 3^-5" "larr# here is our answer!

#log_3 (1/243) = log_3 3^-5 = -5#