In mathematics, many logarithmic identities exist. The following is a compilation of the notable of these, many of which are used for computational purposes.

Trivial mathematical identities are relatively simple (for an experienced mathematician), though not necessarily unimportant. The trivial logarithmic identities are as follows:

By definition, we know that:

$${\displaystyle \log _{b}(y)=x\iff b^{x}=y,}$$

where ${\displaystyle b\neq 0}$ and ${\displaystyle b\neq 1}$.

Setting ${\displaystyle x=0}$, we can see that:

$${\displaystyle b^{x}=y\iff b^{(0)}=y\iff 1=y\iff y=1}$$

So, substituting these values into the formula, we see that: