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Dominic M Sangma
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What is the difference between log and ln??
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Binary Representation: Log or Ln?
- Thread starter Dominic M Sangma
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- Difference Ln Log
In summary: Z80 or the 6502 was better for MS-DOS... :rofl: )In summary, there are two main types of logarithms: common log (log) and natural log (ln). Common log is based on powers of 10, while natural log is based on powers of e (2.71828...). The choice of base can vary depending on the context or author, but generally ln has become the more standard notation. The base of the logarithm may matter in certain calculations, such as determining the number of bits needed to represent something in binary.
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Tom.G
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Log is based on powers of 10, often called Common Log. Ln is based on powers of e (that's 2.71828...), called Natural Log.
By the way, questions should be asked in one of the main Forums. This section is for New Member Introductions. Please read the general information about how things are normally done here. Click on the INFO at the top right of the page.
Oh! And welcome to PF. Hope you find it useful.
Tom
By the way, questions should be asked in one of the main Forums. This section is for New Member Introductions. Please read the general information about how things are normally done here. Click on the INFO at the top right of the page.
Oh! And welcome to PF. Hope you find it useful.
Tom
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mfb
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That depends on the context.Tom.G said:
In physics it is typically base 10, in mathematics it is usually base e, and in computer science it is base 2.
If you want to make the base clear, use lg (10), ln (e) or ld (2).
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I think ##\log = \ln## became more and more the standard, and ##\ln## is a bit old fashioned. A clear line or convention cannot be drawn as it depends on the author what he uses. If no base is mentioned, I'll always vote for base ##\mathbf{e}##, even in CS, because they vary only by a constant factor which usually doesn't play a role, e.g. in runtime calculations.
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mfb
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The base matters if you want to determine e.g. how many bits you need to represent something in binary.
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Yeah, all O(1) to me.mfb said:
I must admit it's a bit of a Bill Gates attitude: "I don't care the hardware."
What is the difference between log and ln?
The main difference between log and ln is the base of the logarithm. Log uses base 10, while ln uses base e (Euler's number). This means that log calculates the power of 10 needed to equal a given number, while ln calculates the power of e needed to equal a given number.
Why do we use logarithms?
Logarithms are useful for simplifying and solving complex mathematical equations. They also help us compare numbers that are very large or very small by condensing them into a more manageable range of values. In science, logarithms are often used to represent exponential growth or decay, and in data analysis, they can help us visualize and interpret data more easily.
Can log and ln be used interchangeably?
No, log and ln cannot be used interchangeably as they have different base values. This means that the calculation and results of log and ln will differ, even if the input number is the same. It is important to pay attention to which base is being used when working with logarithms.
How do I convert from log to ln?
To convert from log to ln, we use the following formula: ln(x) = log(x) / log(e), where x is the number being evaluated. This essentially means dividing the log value by the natural logarithm of 10, which is approximately 2.303. This will give you the equivalent value in ln.
What are the practical applications of log and ln?
Log and ln have many practical applications in fields such as finance, physics, chemistry, and biology. In finance, logarithms are used to calculate compound interest and to evaluate stock market trends. In physics and chemistry, logarithms are used to measure and compare sound, light, and pH levels. In biology, they are used to model population growth and enzyme reactions. Overall, logarithms are useful for analyzing and understanding exponential relationships in various scientific and mathematical contexts.
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