Q.Evaluate:

These are the two standard special values true for EVERY valid base: the log of 1 is always 0, and the log of the base itself is always 1.

(i) $7^0=1$, so $\log_7 1=0$. (ii) $9^1=9$, so $\log_9 9=1$.

(i) $\log_7 1$

Any nonzero base raised to the power $0$ equals $1$: $7^0=1$. By the definition, $\log_7 1=0$.

(ii) $\log_9 9$

Any base raised to the power $1$ equals itself: $9^1=9$. By the definition, $\log_9 9=1$.

Check (independent recomputation): both results match the two general standard values from Section 1 ($\log_a 1=0$ and $\log_a a=1$) directly, for $a=7$ and $a=9$ respectively — no base-specific calculation was even needed.

Swapping the two standard values (answering $\log_7 1=1$ and $\log_9 9=0$) — the log of the NUMBER 1 is always $0$, and the log of the BASE itself is always $1$; these are easy to reverse if not memorised carefully.