Solving Exponential Equations In Quadratic Form - Using Logarithms, With e

This math video tutorial focuses on solving exponential equations in quadratic form. It explains how to factor quadratic expressions and equations in exponential form by factoring by substitution. This video contains plenty of examples and practice problems. It's useful for students taking algebra 2, precalculus, or even college algebra. You need to use logarithms to solve exponential equations. Examples include the base e.
Logarithms - The Easy Way!
• Logarithms - The Easy ...
Log to Exponential Form:
• Writing Logarithmic Eq...
Change of Base Formula:
• Change of Base Formula...
Change of Base Log Problem:
• Logarithms
Properties of Logarithms:
• Properties of Logarithms
____________________________________
Expanding Logarithmic Expressions:
• Expanding Logarithmic ...
Condensing Logarithmic Expressions:
• Condensing Logarithmic...
Natural Logarithms:
• Natural Logarithms
Solving Exponential Equations:
• Solving Exponential Eq...
Exponential Equations - Quadratic Form:
• Solving Exponential Eq...
_______________________________________
Solving Logarithmic Equations:
• Solving Logarithmic Eq...
Graphing Logarithmic Functions:
• Graphing Logarithmic F...
Graphing Exponential Functions:
• How To Graph Exponenti...
Compound Interest Word Problems:
• Compound Interest
Logarithms Practice Problems:
• Logarithms - Practice ...
_______________________________________
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[@TheOrganicChemistryTutor]

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[@veldaasare]

you will never understand how grateful I am for you. You have CARRIED me throughout my high school classes and your content is ageless for the many students in the future that will come in search of desperate help, and you will be here to save them. I can not thank you enough.

[@lihleponzo1650]

Monaka is that you

[@dylam541]

Math hurts my brain or maybe it’s just my professor lol

[@georgesadler7830]

MR. Organic Chemistry Tutor, thank you for another straightforward explanation of Solving Exponential Equations in Quadratic Forms. Logs and Exponentials are common equations in science and engineering.

[@bellatil1270]

Thank you, you saved me from a mental break down kinda:)

[@karenbasaves4741]

Lmaoooo, same!

[@majahantsizwashongwe6426]

Thanks our best teacher...u handled me up during my first semester when things were touph, u just made everything easy for me

[@taqu3trulegacy122]

Very good...

[@freakedoutidiot1178]

Very helpful video 😊

[@ahmedsarker3555]

3:28 why is it ln3 like from where did it came

[@sarastar5348]

😍😍

[@dr916]

I used the quadratic formula in the first example. Took longer but I got the same answer 😅

[@skeptic1101]

you are more helpful than my teacher lmao

[@jimmykai]

for the last example you got 2x=ln8 and 2x=ln6, how were you able to tell that it was 1/2ln8 and 1/2ln6

[@catvyhuynh7359]

I'm sorry for interrupting but what do you mean by the answer of the last example? In my opinion, we are finding the x in the equation 2x = ln8, you can see that the 2x means that 2 multiple x so to find x, we just need to divide ln8 by 2. However, I was quite confused when I solved that example at the first time because I still cannot distinguish the differences between ln and log so I solved it like this: 2x = log2(8) so x = log2(8)/2 = log2(8)/2, = 3/2, so x = 3/2 or 1.5 But I found it incorrect from my calculator so I think that the answer in that video was true.

[@jyl123]

Jeremy Gough 1/2 ln8 =x because ln8 =2x you divide both sides by 2

[@coleabrahams9331]

Regarding 2x=ln(8), if you divide both sides by 2 in order to get x by itself on the left side, you are left with (ln(8) / 2). Since dividing by two is the same as multiplying by 1/2, ln(8)/2 becomes 1/2 (ln(8)). The same theory can be applied to 2x=ln(6)

[@user-mp7wn8tr5g]

​​@@coleabrahams9331But why can't we divide ln8/2 to become ln4?

[@DrexualDesire]

(ln8) /2 = ln√8 ?

[@Mo-bi1pk]

how do you find y then?

[@prishalprince3311]

You cannot find what isnt there......lol

[@irwandasaputra9315]

(e^x-7)(e^x+4)

[@irwandasaputra9315]

(e^x-3)(e^x-2)

[@et8221]

how to solve e^x + e^(1-x) =1

[@adamruggieri3447]

e^(2x) - e^(x) + e = 0; start with that. That's the same thing. Therefore, e^(x) = (1 +/- sqrt(1-4e))/4. Easy. Or, x = the ln of that answer and don't forget to put the absolute value in the argument.

[@johnbuttler915]

what if you can't factor?

[@xFYCNx2]

quadratic

[@usipussi6647]

Use the quadratic formula

[@rifelaw]

Your graph at 6:40 is the wrong way around unless you've flipped the axes. And I'm assuming we're sticking to the standard rule that ln(x) is undefined when x≤0 because we aren't going to Complexland and playing with things like Euler's Identity here. 😉

[@irwandasaputra9315]

(e^2x-6)(e^2x-8)

[@irwandasaputra9315]

e^2x=6 e^x=√6

[@irwandasaputra9315]

e^2x=8 e^x=2√2