Is my proof correct

No.12312549 ViewReplyOriginalReport
Prove:
An integer is a perfect square if k^2=n. If k and m are both perfect squares, then m*k is also a perfect square.
Proof:
Let log base be k
Then log(n)=log(m)=2
Then log(n*m)=2+2(by log product rule)=4=2^2 and thus m*n is also a perfect square

Pic related is me btw