Strange Pattern with Logarithms

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The discussion centers on the observation that the logarithmic values of certain numbers are exactly one unit apart. The user expresses curiosity about the underlying reason for this pattern, specifically in the context of the logarithm base 3. They provide an example showing that log_3(6) can be broken down into log_3(3) + log_3(2), highlighting the relationship between these logarithmic values. The user concludes with a light-hearted acknowledgment of their oversight in recognizing this relationship earlier. This exploration emphasizes the intriguing properties of logarithms and their additive nature.
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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.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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