MHB Simplifying Complex Math Expression

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The discussion centers around simplifying the complex mathematical expression involving square roots and logarithms. Participants clarify the interpretation of the expression, specifically whether it represents 4 plus π squared divided by 9 or the fraction of 4 plus π squared over 9. The focus is on combining logarithmic terms using established logarithm rules to simplify the overall expression. The need for precision in mathematical notation is emphasized to avoid confusion. Clear communication of mathematical expressions is crucial for effective problem-solving.
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$[\sqrt{4+\pi^2}-2\ln\left({\frac{2+\sqrt{4+\pi^2}}{2}}\right)]-[\sqrt{4+\pi^2/9}-2\ln\left({\frac{2+\sqrt{4+\pi^2/9}}{2}}\right)]$
 
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The only thing you can do is combine the logarithms using the logarithm rules.
 
Hello, ineedhelpnow!

You wrote \;4 + \pi^2/9
Does that mean: \:4 + \frac{\pi^2}{9}\,\text{ or }\,\frac{4+\pi^2}{9}\,?
 
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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