$\log_3 4$ and $\log_7 10$: which of these two logarithms is greater?
I figured out that both are between $1$ and $2$, then between $1$ and $1.5$. And then $\log_34$ is greater than $1.25$, and $\log_710$ is smaller than $1.25$. However, that method doesn't work for every example, and I wonder if there's a easier way to solve this?