Question

if log x at base root 2 = a then find the value of log x at the base 2 root 2​

Answer 1

Answer:

$log_{2\sqrt{2}} \ x = \frac{a}{3}$

Step-by-step explanation:

Given :

$log_{\sqrt{2}} \ x=a$

Then,

find the value of :

$log_{2\sqrt{2}} \ x$

Solution :

We know that,

$log_{a^n} \ b=\frac{1}{n}log_{a} \ b$

Also,.

We know that,

2 × √2 = (√2)² × √2 = (√2)³

So,

⇒ $log_{2\sqrt{2}} \ x=log_{(\sqrt{2})^3} \ x=\frac{1}{3}log_{\sqrt{2}} \ b=\frac{1}{3}(a) = \frac{a}{3}$

∴ $log_{2\sqrt{2}} \ x = \frac{a}{3}$

Answer 2

hope you will understand that