Log problems

Question

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687

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+386

HI!

I have a few problems to solve involving logs. Here's one:

I have to write in one log the following:

2log base 5 (3) - 3log base 5 (2)

So far I went like this:

= log5 (3x2) - log5 (2x3)

But that would = 0 wouldn't it? You can't express =0 into one log don't you?

Also, I found this law: log a (p/q)= (loga (p))- (loga (q))

But I don't know how to translate the original equation with that law.

TonyDrummer2 Aug 1, 2016

MaxWong · Answer 1 · 2016-08-01T02:44:04

$\quad\displaystyle2\log_53 - 3\log_52\\ = \displaystyle\log_5(3^2)-\log_5(2^3)\\ = \displaystyle \log_5(\dfrac{9}{8})$

$\boxed {\displaystyle\color{red}a\log b = \log b^a}\\ \color{aqua}and \\\boxed{\displaystyle\color{red}\log a - \log b = \log \dfrac{a}{b}}$

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