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If $3=e^{k},$ determine $k$.

$$1.09861$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 3

The Number $e$

Campbell University

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Lectures

01:39

a. If $e^{t+3}=k e^{t},$ f…

01:58

If $0.5=e^{k},$ determine …

01:10

If $r(k)=\frac{2}{5} k-3,$…

01:03

$$(3 x)^{k}=______…

01:37

If $k=\frac{x+3}{x-3}$ and…

00:43

If $e^{5 t}=k^{\prime},$ f…

01:44

$$\text { If } 5^{3 t}=k^{…

Solve the equation and che…

All right. So in this problem we're trying to solve for K uh, for the exponential function e to the X power. Um, Now, if he used this graphing calculator, this computer algebra system, you can actually just of find that value. Um, but a lot of students don't really understand why that's the correct answer. But the main premises to solve for I should say to the cape power, not X, but if you do actually can actually see the numerical value. But back to the point is toe undo e is to take the natural law, humble sides. The reason for that is natural. Log un does eat their inverse operations. Eso natural really easy, Quito one. So if I do that and I can even make the explanation b x uh, X and what you'll see is that the answer is just going to be X. So, like if I change that value to be three now equal three, it's two equals two. So anyway, the when you undo the natural e you're left with K is equal to the natural laws of three. Whatever you do, the one side you have to do to the other s so that means that K equals natural log of three and we're left with the correct answer. 1.99 If I round 23 decimals. Otherwise you might get a little bit further. 1.98 e can confirm that. That's pretty much correct. Type that in. If I type another equation that said X equals and natural log of three, it's the same value. 1.97 Hopefully, that makes sense.

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