Understanding Logs: Learn How to Calculate Log_10(n)

  • Thread starter quddusaliquddus
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In summary, the conversation discusses a method for deriving the formula n*(9/10)^log_10(n) from the pattern of 9s in the first n numbers. The individual asking the question is struggling with incorporating the logarithm into the formula and is looking for help. They mention wanting to delete the thread and apologize for wasting the expert's time.
  • #1
quddusaliquddus
354
2
Hi.
How would I go from seeing the pattern in the number of nines in the first n numbers, to writing the following formulae for it:

n*(9/10)^log_10(n)

I don't get how to put the log in (or how it works). Sorry, it is an easy question. Please help.
 
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  • #2
One method would be to draw a graph of the number of 9s vs the number n, then fit a curve to it. This would, I think, require a computer since this is obviously not an intuitive relationship.
 
  • #3
I want to delete this thread: Don't know how to!
 
  • #4
way you want to delete it ? :confused:
 
  • #5
I don't need the answer...pls dnt ask y - loong story i'd rather not say.

I apologise for wasting your time.
 

What is a logarithm?

A logarithm is the power to which a base must be raised to produce a given number. In other words, it is the inverse function of exponentiation. The most commonly used logarithm is the base 10 logarithm, also known as the common logarithm.

Why do we use logarithms?

Logarithms are used to simplify complex calculations involving very large or very small numbers. They allow us to transform multiplication and division into addition and subtraction, making it easier to perform calculations. Logarithms are also useful for representing data on a more manageable scale.

How do you calculate a base 10 logarithm?

To calculate the base 10 logarithm of a number, you can use a scientific calculator or a logarithm table. Simply enter the number and press the "log" button on the calculator or look up the corresponding value in the logarithm table.

What is the relationship between logarithms and exponents?

Logarithms and exponents are inverse functions of each other. This means that if you take the logarithm of a number, you can find the exponent that was used to produce that number. Similarly, if you take the exponent of a number, you can find the logarithm of the resulting number.

How can logarithms be used in real life?

Logarithms are used in various fields such as science, engineering, economics, and finance. They are commonly used to measure the intensity of earthquake waves, pH levels in chemistry, and sound levels in music. In finance, logarithms are used to calculate compound interest and in data analysis, they are used to represent data on a logarithmic scale for better visualization.

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