Question

find the value of log 256 to the base√2

Answer 1

Let log root 2(256) = x

         (root 2)^x = 256

         (root 2)^x = 2^8

         (root 2)^x = (root 2)^16

             x = 16.


Hope this helps!

Answer 2

Answer:

$\log_{\sqrt2}(256)=16$

Step-by-step explanation:

Given : Expression $\log_{\sqrt2}(256)$

To find : The value of the expression?

Solution :

Let $x=\log_{\sqrt2}(256)$

Applying trigonometric properties, $\log_a b=x\Rightarrow b^x=a$

Here, $a=\sqrt{2}$ , b=256

$(\sqrt 2)^x=256$

Now we solve for x,

$(\sqrt 2)^x=2^8$

$(\sqrt 2)^x=(\sqrt2)^{16}$

On comparing the base,

$x=16$

Therefore, $\log_{\sqrt2}(256)=16$