If I have log base 2 the square root of c is that the same as log base 2 c to the power of 1/2?

Question

ganeshie8 · Answer

$\large \log_2 \sqrt{c}$

ganeshie8 · Answer

$\large  (\large \log_2 c)^\frac{1}{2} $

ganeshie8 · Answer

your two expressions are like above ?

anonymous · Answer

the first is, I am asking to simplify does it become log2 c1/2 (meaning power of 1/2) if that makes sense

anonymous · Answer

$$\log_{2} c ^{1/2}$$

ganeshie8 · Answer

$\large \log_2 \sqrt{c}$

$ = \large \log_2 (c)^\frac{1}{2}$

$ = \large \frac{1}{2} \log_2 (c)$

ganeshie8 · Answer

yes you're right :)

anonymous · Answer

Ahhhhh thank you :)

ganeshie8 · Answer

np :) we're donw with that.  

but as you can see, below two expressions are not same :-

$\large \log_2 \sqrt{c}$

$\large (\log_2 c)^\frac{1}{2} $

ganeshie8 · Answer

i hope you see why they're not same

anonymous · Answer

No because then if would be squaring the $$\log_{2} c   $$ component yes?

ganeshie8 · Answer

perfect, you mean square rooting !

anonymous · Answer

yes

ganeshie8 · Answer

good :)

anonymous · Answer

Thank you again, I struggle a bit with logs sometimes, I am sure it will make sense one day LOL

ganeshie8 · Answer

logs are tricky in the beginning... but i can see you're pretty good in these :)

anonymous · Answer

hahaha thanks :)

ganeshie8 · Answer

you're wlcme !