Answer
False.
Work Step by Step
$10^3$ is equal to $10\cdot10\cdot10$, which is $1000$. Therefore, $$10^3=1000$$ $$\log 1000 = 3$$ $10^4$ is equal to $10\cdot10\cdot10\cdot10$, which is $10000$. Therefore, $$10^4=10000$$ $$\log 10000 = 4$$ Therefore, $\log 2000$ should be between $3$ and $4$, not less than $3$. Thus, the statement is false.
