Question

find the value of log 8 by root 2​

Answer 1

Answer:

1.4702

Step-by-step explanation:

Log 8 by root 2 = $\frac{log 8}{\sqrt{2} }$

$\frac{log 8}{\sqrt{2} }$ =  $\frac{3log 2}{\sqrt{2} }$

= $\frac{3\times0.693}{1.414 }$

= 1.4702

Answer 2

Answer:

The value of the expression is $\frac{3\log _{10}\left(2\right)}{\sqrt{2}}$ or 0.6386 approximately.

Step-by-step explanation:

Consider the provided expression.

$\frac{log\left(8\right)}{\sqrt{2}}$

8 can be written as 2³

$\frac{log\left(2^3\right)}{\sqrt{2}}$

Apply log rule: $\log _a\left(x^b\right)=b\cdot \log _a\left(x\right)$

$\frac{3\log _{10}\left(2\right)}{\sqrt{2}}$

$=0.63858..$

Hence, the value of the expression is $\frac{3\log _{10}\left(2\right)}{\sqrt{2}}$ or 0.6386 approximately.