I need to prove the continuity of $f(x)=\log x$ using a $\epsilon$-$\delta$ proof

I need to prove the continuity of $f(x)=\log x$ using a $\epsilon$-$\delta$ proof

These is what I have so far but am not sure how to continue

$|\log x-\log a| < \epsilon$

$\log a- \epsilon < \log x < \log a+ \epsilon$

$\frac{a}{e^\epsilon} < x < {a}e^\epsilon$

Any help is appreciated