Question

If log2=0.3 then find the value of log root 2

Answer 1

Given:

(i) The value of log 2 = 0.3.

To find:

(i) The value of log (√2).

Solution:

Given, the value of log 2 is 0.3

According to the laws of logarithm, we know that:

log (a^b) = b log a.   ...(1)

Now, we need to find the value of:

log (√2).

As √2 = 2^(1/2)

So, log (√2) = log (2^[1/2])

This is equivalent to (1), where,

a = 2 and,

b = 1/2.

So,  log (2^[1/2])

= (1/2) log 2

Again, the value of log 2 is equal to 0.3. So,

(1/2) log 2

= (1/2)*(0.3)

= 0.15

Thus, the value of  log (√2) is equal to 0.15