Question

log 512 to the base 2 root 2

Answer 1

$log_{2 \sqrt{2} }(512) = x \\ \\ 512 = {(2 \sqrt{2} )}^{x} \\ \\ {8}^{3} = (\sqrt{8})^{x} \\ \\ {8}^{3} = {8}^{ \frac{x}{2} } \\ \\ 3 = \frac{x}{2} \\ \\ x = 6$

Answer 2

Answer:

$log_{2\sqrt{2}}\,512=6$

Step-by-step explanation:

Given Expression $log_{2\sqrt{2}}\,512$

We have to simplify it.

Use  $log_a\,b=\frac{log\,b}{log\,a}$

$\implies\frac{log\,512}{log\,2\sqrt{2}}$

$\implies\frac{log\,2^9}{log\,2^{1+\frac{1}{2}}}$

$\implies\frac{log\,2^9}{log\,2^{\frac{3}{2}}}$

use   $log\,a^b=b\,log\,a$

$\implies\frac{9log\,2}{\frac{3}{2}\times log\,2}$

$\implies\:\frac{9\times2}{3}$

$\implies3\times2$

⇒  6

Therefore, $log_{2\sqrt{2}}\,512=6$