Log Sums Proof

The sum for logs with the same base goes as the following:

$\log_{n}a+\log_{n}b=\log_{n}{ab}$ .

But how is this property true?

Make $\log_{n}a=x$ and $\log_{n}b=y$ . Now we can see (because of logs work) $n^x=a \text{and}n^y=b$ . If we were to multiply these two values together we would get $n^{x+y}=ab$ . $x+y$ is the sum of our two logs, so were finished. WRONG. We still have a crucial step.