Basic logarithm!

Cal $\begin{aligned}\ \log_{k}1 & = & a \\\log 1 & = & b \end{aligned}$ $\implies k^a=1 \qquad \qquad ... \qquad \qquad 10^b=1$ $\iff k^a=k^0 \qquad \qquad ... \qquad \qquad 10^b=10^0$ $\iff a=0 \qquad \qquad ... \qquad \qquad b=0$ $\iff a \qquad \qquad = \qquad \qquad b$ $\implies \boxed{\log_{k}1=\log 1}$

$\log_k k = 1$ , because when you convert it into index form: $k^1 = k$

There is no such thing as $\log_0$ , therefore $\log_0 1$ is undefined.

$\log_a 1 = 0$ for any $a, a>0, a \neq 1$ . Therefore $\log_k 1 \neq \log 1$ is false.

The true statement is $\boxed{\log_k 1 = \log 1}$

Note: You should state that $k>0,k \neq 1$ for the statements here