Answer
$0$
Work Step by Step
Let $y=\log{5}$.
RECALL:
$y=\log{a} \longleftrightarrow 10^y=a$
Use the definition above to obtain:
\begin{align*}
y=\log{5} \longrightarrow 10^y=5
\end{align*}
Note that:
$10^0=1$ and $10^1=10$
Since
$1<5<10$,
then
$10^0 \lt 10^y \lt 10^1$
Hence,
$0 \lt y \lt 1$
and so
$0 \lt \log{5} \lt 1$.
Checking using a calculator gives $\log{5}\approx 0.6990$
Therefore, the greatest integer that is less then $\log{5}$ is $0$.
