<s>[INST] Logarithmic expression how to simplify $$ \log_{3}24 - 3\log_{3}5\times \log_{5}2$$
What I can get is:
$$ \log_3{24} - \log_3{5^3} \times \log_{5}2$$
Change of base rule to get it all in base 3:
$$ \log_5{2} = \frac{\log_3{2}}{\log_3{5}} $$
Now I have:
$$\log_3{24} - \frac{\log_3{5^3}\times \log_3{2}}{\log_3{5}}$$
How to continue from here?
 [/INST] $$\begin{align}\log_3{24} - \frac{\log_3{5^3}\times \log_3{2}}{\log_3{5}}&=\log_3{24} - \frac{3\log_3{5}\times \log_3{2}}{\log_3{5}}\\
&=\log_3{24} - 3\log_3 2\\
\end{align}$$
Now you can use the exponent law again on the second term, and then the additive law. Can you finish from here?
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