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

Question

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 $10$).

score 2 · Accepted Answer · answered Nov 09 '13 at 07:29

2

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

answered Nov 09 '13 at 07:29

Lord Soth

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Thanks so much. I completely remember now – Red Queen10101 Nov 09 '13 at 09:16
@RedQueen10101 You are welcome. – Lord Soth Nov 09 '13 at 09:16

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

1 Answers1