(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given that

[tex]\log_{4n} 40\sqrt {3} = \log_{3n} 45[/tex]

find

[tex]n^3[/tex]

2. Relevant equations

Logarithm properties

3. The attempt at a solution

I can get an expression for n but looks messy, and suspect there is probably a more compact answer. This is what I did:

[tex] \dfrac{\log 40\sqrt{3}}{\log 4n} = \dfrac{\log 45}{\log 3n}

\leftrightarrow \dfrac{\log 40\sqrt{3}}{\log 45} = \dfrac {\log 4n}{\log 3n}

= \dfrac{\log 4 + \log n}{\log 3 + \log n}[/tex]

and then I solved for log n; but again, my answer is 'messy'.

Thanks for any help.

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# Homework Help: Logarithm expression is messy

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