In this video I solve 3 equations that involve base e exponential functions using natural logarithms. Example 1 at 1:02 Example 2 solved with 2 methods are at 6:18 and 11:24 Example 3 solved two ways at 13:56 and 17:10

I got some more great suggestions for solving my examples from Jay Ballauer,
Second Example:
Rewrite e^2x at power-of-a-power (e^x)^2 first…then you have a pair of e^x, which you let u = e^x. That let’s students see the quadratic because they see e^x as replaceable (there are two of them, which is easy to see). Once you work u^2 -6u-7 = 0 as a quadratic, you can then replace u with e^x at the end of the problem for both solutions.

It’s much cleaner that way and its a helpful method for many types of problems…like when they see the same thing with trig functions in a couple of months. Of course you don’t have to use “u” as a variable, but its traditional for substitution.

Third Example:
On the third example, you can just divide both sides by e^(1-x) from the beginning. For the left side you get e^(3x+1)/e^(1-x) which is simple division of same bases…so you subtract powers to get e^(3x+1-(1-x)), or just e^4x (watch out for the distribution of negative there). So, you get to e^4x= 6 after a couple of easy steps.

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Amazing, Life Changing Tutor
Before I met Jonathan, I was struggling through most of my STEM classes because I was simply not studying properly. He taught me all kinds of new study habits that would help me to save time, raise my grades, and lower my stress. Jonathan was specifically tutoring me in vector calculus and is an amazing tutor on the subject. You will walk away from a lesson with a game plan knowing exactly what you need to do before your next session with him or before your next exam in order to do well in the course. I highly recommend him as a tutor.