54 lines
2.3 KiB
Markdown
54 lines
2.3 KiB
Markdown
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---
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title: Intro to Logarithms
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---
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## Intro to Logarithms
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Logarithms are mathematical functions used to find what power a base is raised to in order to receive a specific output.
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*Here in the example variable b is the base whereas variable a is the desired output and variable c is the exponent.*
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Logs are used in various things in the real world. They are used in the pH scale, the measuring of the intensity of earthquakes (the Richter Scale) and many other things.
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Example of logs in python:
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```python
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import math
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# math.log(value, base) - outputs exponent
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math.log(100, 10) #outputs 2
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math.log(2, 2) #outputs 1
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```
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#### Sources:
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<!-- Please add any articles you think might be helpful to read before writing the article -->
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* https://betterexplained.com/articles/using-logs-in-the-real-world/
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* https://www.khanacademy.org/math/algebra2/exponential-and-logarithmic-functions/introduction-to-logarithms/a/intro-to-logarithms
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### Definition of logarithm
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The logarithm of a number __x__, written _log(__x__)_, usually means the number you have to use as power over 10 to get __x__. Let's say you wanna find _log(10)_. This means you wanna find the number you have to raise 10 to to get 10. This gives us an equation:
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_log(10) = x_.
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We can use this and apply it as a power of 10 on both sides. This changes the equation to:
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_10<sup>log(10)</sup> = 10<sup>x</sup>_
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The _10<sup>log(__x__)_</sup>, where __x__ is any number, will return __x__, as _10<sup>log</sup>_ cancels out. This means our equation is now
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_10 = 10<sup>x</sup>_
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Given that _10<sup>x</sup>_ is equal to 10 times itself _x_ times, it means that 10 needs to be multiplied with itself enough times to be exactly 10, and _x_ is therefore 1. This is because
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_10<sup>1</sup> = 10_
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### Definition of the natural logarithm
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This is strictly the same as the definition of logarithm, except what numbers are used. In the normal logarithm, the base number is usually 10, wheras in the natural logarithm, often written _ln_, uses _e_, euler's number as base. This means that
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_ln(e) = 1_, instead of _log(10) = 1_.
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So, we are instead finding the power you need to raise _e_ to in _ln(__x__)_.
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