Strange Pattern with Logarithms

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SUMMARY

The discussion centers on the logarithmic identity involving base 3, specifically the equation $\log_3(6) = \log_3(3) + \log_3(2)$. Participants noted that $\log_3(3)$ equals 1, leading to the conclusion that $\log_3(6)$ is exactly 1 unit greater than $\log_3(2)$. This relationship highlights the additive property of logarithms when decomposing numbers into their prime factors. The realization of this property prompted a sense of enlightenment among participants.

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ConstantineO
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I was crunching through some logarithm questions for homework when I noticed this. I was wondering if any of you have any incite on what causes these two numbers to be exactly 1 unit apart from each other. I found it very odd, and I am wondering if there is some kind of relation here that I am not aware of. Get back to me when you can.
 
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$$
\log_3(6) = \log_3(3 \times 2) = \log_3(3) + \log_3(2) = 1 + \log_3(2)
$$
 
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DrClaude said:
$$
\log_3(6) = \log_3(3 \times 2) = \log_3(3) + \log_3(2) = 1 + \log_3(2)
$$
I feel very foolish now hahaha. Why did I not see that.
 

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