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(a) What is the natural logarithm?(b) What is the common logarithm?(c) Sketch the graphs of the natural logarithm function and the natural exponential function with a common set of axes.
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02:40
Jeffrey Payo
01:42
Heather Zimmers
Calculus 1 / AB
Calculus 2 / BC
Calculus 3
Chapter 1
Functions and Models
Section 5
Inverse Functions and Logarithms
Functions
Integration Techniques
Partial Derivatives
Functions of Several Variables
Johns Hopkins University
Harvey Mudd College
Baylor University
University of Nottingham
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Alright, let's take a look at the difference between natural logs and common logs. So natural logarithms and common logarithms. The biggest difference is the base, let's take a look at the natural log that is log base E of acts or Ln of X. But both of those mean the same thing. Common logarithms. The only difference is now we're looking at base 10 um and you'll if you see it without base then it is actually still base 10. So log of X is the same as log base 10 of X. Just like natural log of X is the same as log base E of X. Remember with log rules we can write this as either the Y equals X and for common log we can write it as 10 to the Y equals X. So these are equivalent statements and just one last note is super cool. That exponential functions are inverse to log functions so for example, E to the X. That's exponential growth naturally occurring. If I rotate the curve around white balls X. I get the inverse function which is Ln of X. And you can see the symmetry. So. Very cool. Alright. Have fun with logs. See you next time
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