Expanding logs

Question

Hi, I just want to know if if my answer is correct. 

 

log n√(100x³/y^m) 

 

* Instead of it being squared, its an n. Also (100x³/y^m) is under one big root*

 

The answer I got is : 

 

n+ nlog(x) + (1/n)log — (m/n)log(y)

Answer 1

log ⁿ√(100x³/y^m)

log (100x³/y^m)^1/n

(1/n)(log 100x³ - log y^m)

(1/n)(log 100 + log x³ - m log y)

(1/n)(2 + 3 log x - m log y)