Why does log(25^1/2) covert to log(*square root*25)

Question

So there's this question. It's 1/2log(25)+log(4). Then we convert it to log(25^1/2) + log (4). But then the log converts to the square root of 25 from log(25^1/2). Why? And what does that mean if, per se, we have the question of 1/3log(8)+log(16)? 

Answer 1

In general, x = a^y is the exponential form of y = log_ax

 

It can easily be verified that 1/2 * log 25 = log √25 = log 5 = 0.699

 

Consequently, 1/3 * log 8 = log³√8 = log 2

 

Remember also that log a + log b = log (ab)