# Math Help - Natural Logarithms...

1. ## Natural Logarithms...

Can anyone explain Natural Logarithms, such as when it is appropriate to use them, how to use them, and anything you may need to know in order do to NL questions or anything related to them. Thanks

2. Originally Posted by hamnet
Can anyone explain Natural Logarithms, such as when it is appropriate to use them, how to use them, and anything you may need to know in order do to NL questions or anything related to them. Thanks
Use wikipedia for a formal definition.

Natural logarithm - Wikipedia, the free encyclopedia

Suppose you have e^(2x + 3) = e^(50x) and you wanted to solve for x;

In order to negate the e's, you would use ln;

ln(e^(2x + 3)) = ln(e^(50x))

2x + 3 = 5x

Further, ln(x) is an exponential function.

It crosses the x-axis at (1,0), (whereas e^(x) cross the y axis at (0,1).

There are are many uses for the natural log. Take a look at the wikipedia site and then list any questions you have thereafter.

3. Originally Posted by hamnet
Can anyone explain Natural Logarithms, such as when it is appropriate to use them, how to use them, and anything you may need to know in order do to NL questions or anything related to them. Thanks
The natural logarithm is exactly like the average logarithm $\log$. But this one just has a different base.
$\log_e = \ln$
The base is a number called $e\approx 2.718$.
Thus,
$\ln 5 = \log_e 5$
Meaning what does $e$ have to be raised to, to result in 5?
You may wonder why such a strange number, but it is important when you learn the Calculus.

4. Originally Posted by AfterShock
Use wikipedia for a formal definition.

Natural logarithm - Wikipedia, the free encyclopedia

Suppose you have e^(2x + 3) = e^(50x) and you wanted to solve for x;

In order to negate the e's, you would use ln;

ln(e^(2x + 3)) = ln(e^(50x))

2x + 3 = 5x

Further, ln(x) is an exponential function.

It crosses the x-axis at (1,0), (whereas e^(x) cross the y axis at (0,1).

There are are many uses for the natural log. Take a look at the wikipedia site and then list any questions you have thereafter.
Does 50x become 5x? or was that just a typo?

--- When it comes to Algebra, when do you know that you need to use a Natural Log?