Question

find the value of log 512 baseroot2

Answer 1

Let x = log of 512 base √2
(√2)^x = 512
xlog(√2) = log(512)
x = log(512)/log(√2)
x = 18
(√2)^18 = 512

Answer 2

$log_{ \sqrt{2}} 512$
$log_{ 2^{ \frac{1}{2} } } (2^9)$

We know that
$log_{ x^{ n } } (y^m) = \frac{m}{n} log_{x}y$

Therefore,

$\frac{9}{ \frac{1}{2}} log_{2}2$

18