Question

find the value of log8/root2​

Answer 1

Answer:

$\log (\frac{8}{\sqrt2})=0.752$  

Step-by-step explanation:

Given : Expression $\log (\frac{8}{\sqrt2})$

To find : Evaluate the expression ?

Solution :

We know, $\log(\frac{x}{y} )=\log x-\log y$

Applying in given expression,

$\log (\frac{8}{\sqrt2})=\log 8-\log \sqrt2$

$\log (\frac{8}{\sqrt2})=\log 2^3-\log 2^{\frac{1}{2}}$

Applying logarithmic property, $\log a^x=x\log a$

$\log (\frac{8}{\sqrt2})=3\log 2-\frac{1}{2}\log 2$

$\log (\frac{8}{\sqrt2})=(3-\frac{1}{2})\log 2$

$\log (\frac{8}{\sqrt2})=\frac{5}{2}\log 2$

Using log table,

$\log (\frac{8}{\sqrt2})=\frac{5}{2}\times 0.301$

$\log (\frac{8}{\sqrt2})=0.752$

Answer 2

Answer:  The required value of the given expression is 0.64.

Step-by-step explanation: We are given to find the value of the following logarithmic expression :

$E=\dfrac{\log8}{\sqrt2}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We will be using the following property of logarithms :

$\log a^b=b\log a.$

From expression (i), we get

$E\\\\=\dfrac{\log 8}{\sqrt2}\\\\\\=\dfrac{\log2^3}{\sqrt2}\\\\\\=\dfrac{3\log 2}{\sqrt2}\\\\\\=\dfrac{3\times .30103}{1.414}\\\\\\=\dfrac{0.90309}{10.414}\\\\=0.6387\\\\\sim 0.64.$

Thus, the required value of the given expression is 0.64.