simplify log(x^2)-log(xy)+4log(y)

We can use the facts that

1. log(a) + log(b) = log(a*b)

2. log(a) - log(b) = log(a/b)

3. log(a^b) = b*log(a)

 

log(x²) - log(x*y) +4 log(y) → log(x²/(x*y)) + log(y⁴)  → log(x²*y⁴/(x*y))  → log(xy³) → log(x) + log(y³)  → log(x) + 3log(y).

 

You can stop at whatever expression you think is the simplest!

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