1. The problem is to understand the logarithm of numbers less than 1. 2. Recall the definition of logarithm: for $\log_b(x)$, it answers the question "to what power must we raise $b$ to get $x$?" where $b>0$ and $b \neq 1$. 3. When $0 < x < 1$, the logarithm $\log_b(x)$ is negative because raising $b$ to a negative power gives a fraction between 0 and 1. 4. For example, if $b=10$ and $x=0.1$, then $\log_{10}(0.1) = -1$ because $10^{-1} = 0.1$. 5. In general, for any base $b>1$, if $0 < x < 1$, then $\log_b(x) < 0$. 6. This is a key property of logarithms: logarithms of numbers less than 1 are negative. Final answer: For $0 < x < 1$ and base $b>1$, $\log_b(x) < 0$.