Question

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

Answer 1

`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`