What are the basics of logarithmic functions?

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Logarithmic functions express relationships between numbers in exponential form, where log base a of x equals y translates to x being equal to a raised to the power of y. The correct notation is log_a(x) = y, which is equivalent to a^y = x. The discussion highlights a common misunderstanding in the notation, emphasizing the importance of accuracy in mathematical expressions. A participant pointed out an error in the initial explanation, leading to clarification. Understanding these basics is essential for students learning about logarithmic functions.
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This is just some information on log functions.
log base a x = y is translated x is equal to b to the y power.

Just a little tid bit of information for all of those curious math students.
 
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Don't you mean a to the power of y?

logax=y <--> ay=x
 
Yes you are right, I made a little mistake! Thanks for correcting me.
 
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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