While solving the following logarithm question: $\frac{\log_3 135}{\log_{15} 3}\ - \frac{\log_3 5}{\log_{405} 3}\\$ I came to the point where I have to multiply two equal log: $\log_3 135.\log_3 15 - \log_3 5.\log_3 405$. Is there any way to multiply two log.
2026-03-24 22:01:27.1774389687
Question about multiplication/divisions of logarithms
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$$\log_3 135.\log_3 15 - \log_3 5.\log_3 405=? $$
Note that $$135=5(27)\implies \log_3 135 =3+ \log_35 $$
Similarly $$\log_3 15= 1+\log_3 5 $$ and so forth.