How do you take the natural logs?

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In summary, the conversation is about taking natural logs and differentiating them. The first speaker is struggling with understanding the basic concepts and the steps involved in taking natural logs. The second speaker offers a suggestion to simplify the logarithm by using the property log(xy)=log x + log y. They also question what the product is being evaluated with respect to.
  • #1
semidevil
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how do you take the natural logs??

I think this is why I can't do my problems, maybe I'm missing some basic concepts.

ok, so let [tex] L({\theta}) = \theta^{-2n} \prod y e^{-(1/theta)}\sum y [/tex]

taking the natural log, I get

[tex]ln L(\theta) = -2nln\theta + ln \prod y - 1/\theta \sum yi [/tex].

I don't know, how did they do that?

and later, I will need to differentate it too, but and I don't know how to do it either. but for that one, how did they do it?
 
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  • #2
I can't make sense of what you've written. Indices and parentheses would help. Anyway, whatever that first expression is supposed to be, there's a good chance you will be able to simplify the logarithm considerably by using log(xy)=log x + log y repeatedly.
 
  • #3
That product wrt what is it evaluated...?

Daniel.
 

Related to How do you take the natural logs?

1. What is the natural logarithm?

The natural logarithm, denoted as ln, is a mathematical function that is the inverse of the exponential function. It is used to determine the time needed to reach a certain level of growth or decay.

2. How do you take the natural logarithm of a number?

To take the natural logarithm of a number, you can use a scientific calculator or a mathematical formula. On a calculator, you would press the "ln" button and enter the desired number. The formula for calculating the natural logarithm is ln(x) = loge(x), where e is the mathematical constant approximately equal to 2.71828.

3. What is the difference between natural logarithm and common logarithm?

The natural logarithm uses the base e, while the common logarithm uses the base 10. This means that ln(x) is the power to which e must be raised to equal x, while log(x) is the power to which 10 must be raised to equal x.

4. What are the applications of natural logarithm in science?

Natural logarithm is commonly used in scientific fields such as biology, chemistry, and physics to model exponential growth and decay. It is also used in statistics to measure the spread of data and to transform skewed data into a more normal distribution.

5. Can the natural logarithm of a negative number be taken?

No, the natural logarithm can only be taken for positive numbers. Attempting to take the natural logarithm of a negative number will result in an error. This is because the output of the natural logarithm function is always a positive number.

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