What is #log_3 243#?

3 Answers
Jan 1, 2017

#log_3 243 = 5#

Explanation:

Let #x = log_3 243#

#:. 3^x = 243 = 3^5#

Equating indices#-> x=5#

Aug 5, 2018

#5#

Explanation:

We can rewrite #243# as #3^5#. We now have

#log_3 3^5#

We can now cancel the base-#3#s to get

#log_cancel3 cancel3^5=>5#

We can check this by confirming that #3^5=243#.

#3^5=9*9*3=81*3=243#

We do indeed get #5#.

Hope this helps!

Aug 5, 2018

#color(green)(log_3 243 = 5#

Explanation:

https://mathsmethods.com.au/vce-maths-methods-lessons-cheatsheets/vce-maths-methods-logarithm-laws/

#log_3 243 = log_3 (3^5)#

#color(crimson)("Applying rule "log_a (m^p) = p log_a m#

#=> 5 log_3 3#

#color(maroon)("Applying rule "log_a a = 1#

#color(green)(=> 5#