What is the curious relationship between exponential and logarithmic functions?

In summary, an interesting math observation is a unique or unexpected discovery or pattern found in mathematics. To make one, you can explore different mathematical concepts and look for connections or solve challenging problems. Examples include the Fibonacci sequence, Golden Ratio, Mandelbrot set, and the concept of infinity. These observations are important for understanding the world and advancing various fields. They can also be applied in daily life to solve problems and improve critical thinking.
  • #1
drag
Science Advisor
1,105
1
Greetings !

Maybe I'm just too tired and missing something, but this strange thing
occured to me:
a^n + b^n = c^n
ln( a^n + b^n ) = n * ln ( c )
a^n + b^n =/= e^n * c
example: a = 3; b = 4; c = 5; n = 2; 25 =/= e^2 * 5

Live long and prosper.
 
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  • #2
What's strange about it?
 
  • #3
this =/= is approximately?
 
  • #4
ah... sorry, like I said I AM very tired, I see it now, foolish of me... :biggrin:
 
Last edited:

1. What is an interesting math observation?

An interesting math observation is a discovery or pattern found within the realm of mathematics that is unique or unexpected. It could be a connection between two seemingly unrelated concepts, a curious number sequence, or a mathematical phenomenon that defies intuition.

2. How can I make an interesting math observation?

To make an interesting math observation, you can start by exploring different mathematical concepts and looking for patterns or connections between them. You can also try to solve challenging math problems or experiment with different mathematical operations to see if any interesting patterns emerge.

3. What are some examples of interesting math observations?

Some examples of interesting math observations include the Fibonacci sequence, where each number is the sum of the two preceding numbers, and the Golden Ratio, which appears in many forms in nature and art. Other examples include the Mandelbrot set, fractals, and the concept of infinity.

4. Why are math observations important?

Math observations are important because they help us understand the world around us and make sense of complex phenomena. They also play a crucial role in the development of new mathematical theories and applications, leading to advancements in various fields such as science, technology, and engineering.

5. How can I use interesting math observations in my daily life?

You can use interesting math observations in your daily life by applying them to real-world problems or using them to improve your critical thinking and problem-solving skills. You can also use them to appreciate the beauty and logic behind mathematical concepts and their applications in our everyday lives.

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