How do I express this as a single logarihm (condense) ?

Question

1/2Log(x) + 3/2Log(2y) — log(x²y) 

 

Can you please show me steps? I tried at least five times and the book says the answer is with a square root but I dont know how to get there. 

 

The first thing I did was use power property but after this is when Im confused. 

Answer 1

1/2Log(x) + 3/2Log(2y) — log(x²y)

This is an example the fact that the log of a product is the sum of the individual logs of its factors,

and the log of a quotient is the difference of the logs of the numerator  denominator. Plus the factors in front of logs can be puton top of the arguments,

 

So the first simplification is: Log(x^½) + Log(2y)^(3/2) — log(x²y)

 

Next, Log [(x^½)(2y)^(3/2)] — log(x²y)

 

Condensing this diffrence of logs: Log [(x^½)(2y)^3/2 ÷ (x²y)]

and if you wish you can further simplify the expression within the bold square brackets.