Log/Exponential properties

[AbbyANoble]

We note that $\log_b b^x = x$ and $\log_b 1 =0$ in Remark 5.3.9.

I think we should also point out that $b^{\log_b x} =x$. Maybe this and $\log_b b^x = x$(along with their natural log counterparts) should be together in a remark pointing out that they are a result of logs and exponentials being inverse functions.

Then $\log_b 1 =0$ and $\ln 1 =0$ could be pointed out too. Not sure what they are officially called? Logs involving 1?

Editing to add that we also need to point out that $\log_b b =1$ and $\ln e = 1$. These (and the ones in the previous paragraph) can both be discovered through an activity using the concept of logs, but at some point we need to write them down.