Mathematics

The key insight is that logarithms with a base between 0 and 1 flip inequalities—they're decreasing functions. Since $\log_{1/2}$ has base $\frac{1}{2} < 1$, a larger input gives a smaller output. Because $3 < 5$, we have $\log_{1/2}3 > \log_{1/2}5$. Think of it as: you're asking "what power of $\frac{1}{2}$ gives me 3 versus 5?"—you need a less negative exponent for the smaller number.

The key insight is that logarithms with a base between 0 and 1 flip inequalities—they're decreasing functions. Since $\log_{1/2}$ has base $\frac{1}{2} < 1$, a larger input gives a smaller output. Because $3 < 5$, we have $\log_{1/2}3 > \log_{1/2}5$. Think of it as: you're asking "what power of $\frac{1}{2}$ gives me 3 versus 5?"—you need a less negative exponent for the smaller number.