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

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Answer 1 · 2016-06-09T06:34:27

$6$

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

Alternatively, use the change of base formula:

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

to find:

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

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