Q:

How should I express one $\log$ in terms of others?

Can someone please help me with this logarithmic question? I know it’s easy, but I need to refresh my memory on how to do it.

If $X=\log2$ and $Y=\log3$, express $\log0.6$ in terms of $X$ and $Y$ (assume all logs have a base of $10$).

A:

All you need to know is $\log(ab) = \log a + \log b$. Then, $\log 0.6 = \log(2\times 3\times \frac{1}{10}) = \log 2 + \log 3 + \log \frac{1}{10} = X+Y-1.$

