Question

Find the value of log(sqrt(16))/log 16

Answer 1

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Answer 2

Answer:

$\frac{\log (\sqrt{16})}{\log (16)}=\frac{1}{2}$

Given:

$\frac{\log (\sqrt{16})}{\log (16)}$

Solution:

The square root is equal to the half of the value.

Now, the square root is taken as:

$\sqrt{a}=a^{1 / 2}$

Now, the given expression becomes,

$\Rightarrow \frac{\log (\sqrt{16})}{\log (16)}=\frac{\log (16)^{1 / 2}}{\log (16)}$

Now, on applying the logarithm on power.

The logarithm of the quantity with power ‘n’ is equal to the n times of the logarithm of the quantity.

$\log _{e}\left(a^{b}\right)=b \log _{e} a$

On applying the above function in the given expression,

$\Rightarrow \frac{\log (\sqrt{16})}{\log (16)}=\frac{(1 / 2) \log (16)}{\log (16)}$

$\Rightarrow \frac{\log (\sqrt{16})}{\log (16)}=\left(\frac{1}{2}\right) \frac{\log (16)}{\log (16)}$

On cancelling the same values,

$\therefore \frac{\log (\sqrt{16})}{\log (16)}=\frac{1}{2}$