What is #log_3 243#?

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Answer 1 · 2017-01-01T03:20:12

#log_3 243 = 5#

Let #x = log_3 243#

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

Equating indices#-> x=5#

Answer 2 · 2018-08-05T02:44:54

#5#

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!

Answer 3 · 2018-08-05T03:00:15

#color(green)(log_3 243 = 5#

#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#