How do you calculate #ln(4096)/ln(4)#?

1 Answer
Jun 9, 2016

Answer:

#6#

Explanation:

#ln(4096)/ln(4) = ln(4^6)/ln(4) = (6 color(red)(cancel(color(black)(ln(4)))))/color(red)(cancel(color(black)(ln(4)))) = 6#

Alternatively, use the change of base formula:

#log_a b = (log_c b) / (log_c a)#

to find:

#ln(4096)/ln(4) = log_4 4096 = log_4 4^6 = 6#