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Numerade Educator

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Problem 34 Hard Difficulty

(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.

Answer

a) $\ln x=\log _{e} x$
b) $\log _{10} x$
c) See graph

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Video Transcript

natural log and common log are both used a lot natural log means log based e So the notation for natural log of X is Ln x, and it's the same as log based E of X. Common law is law based. 10. We write it Just log of X. We don't put a base there, but it means log based 10 of X. Now what are the graphs look like? So if we were to picture Y equals natural log of X, let's imagine a couple points that we can plot. For example, if X is one, we have the natural log of one, and that would be zero because e to the zero gives us one. And what if X is E? Then the y value would be one, because the natural log of E is one each of the first power is he. And how about some points on why equals log based 10 of X common log. If X was one, then log of one would be zero because tend to the zero is one. Same as the other graph and effects was 10 the white corn. It would be one because 10 to the first power gives us 10. So we could plot these points for the natural law graph. We have 10 and we have E, which is approximately 2.7. So e one and the graph looks like this. And for the common law graph, we had the 0.10 again, Same point. And we have the 0.10 1 so the graph looks like this.