1. The problem is to understand the logarithm of numbers greater than 1. 2. Recall that the logarithm function $\log_b(x)$ answers the question: "To what power must the base $b$ be raised, to get $x$?" Here, $b$ is the base of the logarithm, and $x$ is the number whose logarithm we want. 3. When $x > 1$ and $b > 1$, the logarithm $\log_b(x)$ is positive because raising $b$ to a positive power results in a number greater than 1. 4. For example, if $b=10$ and $x=100$, then $\log_{10}(100) = 2$ because $10^2 = 100$. 5. More generally, if $x > 1$, then $\log_b(x) > 0$ for any base $b > 1$. 6. This means the logarithm of numbers greater than 1 is always positive when the base is greater than 1. Final answer: For $x > 1$ and $b > 1$, $\log_b(x) > 0$.