Solving Exponential and Logarithmic Equations
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- Опубликовано: 3 окт 2024
- Now that we know how to use logarithms, we are ready to solve a whole new class of equations that we couldn't before! Whether these are logarithmic equations or exponential equations, using logs will allow us to get the answers we need.
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Whoops, at 5:51 I display two solutions for an equation, one positive and one negative, but the negative solution actually does not work because you can't take the log of a negative number! So only the positive solution works there, sorry for any confusion caused.
Professor Dave Explains there is also one mistake at the very end of the video at 6:23 for ln(x+1)^2=2. There should be two answers, which is -1 plus or minus e. The negative sign comes from the one when you take the square root of both sides. When you plug in -1-e in the original equation, squaring the negative value will still yield positive answer. For example, (-1)^2=1 and 1^2=1. In case you didn’t see the properties of logarithms of the even powers, it would be ln(x+1)^2=2ln(abs(x+1)). abs stands for absolute value. The absolute value is there because the value can be negative at that value. If there’s no absolute value there, it would make the answer undefined.
log₂(-1) = log₂(-1×1)=log₂(-1)+log₂(1)
log₂(-1)+log₂(-4)=log₂(-1×-4)=log₂(4)=2
log₂(-1)+log₂(-4)=
log₂(-1)+log₂(1) + log₂(-1)+log₂(4) =
log₂(-1×-1)+log₂(1)+log₂(4)=2
Hie to my teacher
I guess it is kind of randomly asking but does anybody know of a good website to watch new series online?
@Hassan Ruben I dunno I would suggest Flixportal. you can find it on google =) -kyng
profesor dave's intro is what gives me hope.
I literally stopped going to my coaching institute and I feel I learn more from you, thanks professor dave!
POV: you just wanna learn logarithmics, and you met jesus christ instead.
Pov pov pov cells pov Jesus interlinked pov cells interlinked pov pov
Pov that feelings when your just wanted to know more logarithmische in mathimatik but instead meeting Jesus the messiah!😂😂
Wow, that's not a good comment. 👎
😂😂
And that makes you to even understand more 😅
Thank you so much for ur vids i didn't take maths in my 11th grade so learning these concepts will help me alot to understand some parts in physics and chemistry 😀❤️
"And if we stare at this for a few seconds, we can see..." 5:41 😂🤣🤣, awesome technique: stare at equations. This is the best part of the video.
Your videos are awesome Professor Dave!
And I literally did it🤦♀️🤦♀️
Great explanation and engaging graphics! Good job, Professor Dave!
At 5:50 x cannot be -1 since log2 (-1) is undefined for negative values of x.
ah mannnn! yeah. you're totally right. thanks for pointing that out.
@@ProfessorDaveExplains it's strange because when we compensate (-1) in the second expression after we condensed it, it's fine! but in the first expression (expanded) it's not valid as Teen pointed out.
Is this called as Critical Numbers?
Bro you are insanely clever teacher thanks for every thing (I like the way you teach)
This video was very fun to follow along with, got to practice some log
wouldn't -1 be extraneous?
Logarithm made simple thank you sir.
Thanks professor
what is the definition of a logarithm that makes 2 square or 4 = x square - 3x , how did you get the 4
Thanks prof
can someone explain to me if a question: logx 4³ - logx 2 = 5?
What does that "In" mean??
natural log! check out the three part series i did on logarithms that was released just before this one.
Professor Dave Explains Thanks
MILTIADIS POLITIS
It's the natural logarithm. Basically, log to the base of e.
I'm kinda desperate now because my quiz in this subject will be tomorrow and Professor Dave explained it in detail.
Thanks, Jesus
Same here, I’ve had a sub the past month and she’s really old and had to teach us this. Made no sense, and of course I’m only gonna try and actually learn it last minute now
All was good until I had to solve them yikes
6:24 how is log (3x-2)= 1 giving us x=4 ????
when we reach 10=3x-2 give us the following procedure
3x = 10-2
3x = 8
3x/3 = 8/3
x = 2 (2/3) ????
pls explain how the 4 was obtained from ur solution
It was solve like this:
3x -2-10=3x-12=0; Which is equal to 3x=12 Then x =4
Hi professor,
Can I also use the common log in the place of the natural log in problem number 4??
no you can't, you can think of ln (log natural) as log e (x)
so to cancel it out you need to use e
e log e (x) = x
What is the solution of 9^2x-1 =36x
in the last question of the comprehension, it can be (-e -1) as well
yes you're right👍
Well done teacher
i understood his explanation and such but i couldnt answer the reading comprehension oh my gosh my calculus exam is tom. and its now 12 am midnigbt
Well this isn't even calculus, it's algebra, so it sounds like you might be in a lot of trouble!
@@ProfessorDaveExplains omggg reallyyy aa but why is this whatmy calculus teacher lectured to us
I dunno what to tell you, this isn't calculus.
@@ProfessorDaveExplains i just got home from school and i just finished the exam! this video of yours actually helped tho even if the exam was calculus skskksks
Well, that's good news then! Make sure to keep watching through my mathematics playlist so that you're never in trouble again!
When we use ln and log Mr. Dave..?
You can use either one as long as the base are the same. On your calculator, we only have common log (log base 10) and natural log (log base e). A logarithm without a subscript is referred to a common log (written as “log” on your calculator). log base e of x is the same as natural log (ln). Usually, we use ln only if the base is e and common log if the base is 10.
explanation as lucid as clear running water
For the comprehension problems, how did you get from log(3x-2)=1 to 10=(3x-2)? Did you apply log base 10 to both sides of the equation?
it's just the definition of a log, the base of the log raised to the power of what's on the other side of the equals sign is equivalent to what the log is operating on.
If there’s no subscript written in the logarithmic form, it refers to the common log or log base 10.
@@ProfessorDaveExplains why is log 1 euqals to 0 but 10 in this equation?
@@phewpheww4599 there's a few parts to this answer.
log(1) does = 0. Log(1) = x is asking you to find what number, if the base 10 was raised by this number, would be equal to 1? By the laws of exponents, any number raised to 0 will equal 1. Any base log will do the same. Log3(1) =0, log999(1) = 0.
The answer to the third question, log(3x-2) = 1, has nothing to do with that rule. The 1 is already equal to the left side of the equation, the question is not asking you to find out what log(1) = x is.
In the third question, we can express the 1 on the right as log(10), so it has the same base as the left side. Because log10(10) is equal to one, log(10) can be substituted for 1. To confirm that, solve log10(10) = x, which is asking by what number 10 needs to be raised by to equal 10. 10^1 = 10, so the answer is 1.
Then we have log(3x-2) = log(10). As we have log on both sides, they can be cancelled out, leaving
3x-2 = 10. Balance by adding 2 to both sides.
3x = 12. Divide by 3.
X = 4.
I could be wrong but that's how I understand it.
The last equation of the comprehension Check is wrong ist should be x = e^root(2) -1
The video is correct.
youre my hero bro
why your video can't be download
Professor, in 6:29 I didn't understand the solution of ln(x+1)^2=2 can you please explain it?
Thank you
The answer actually has two solutions because when you take the square root of both sides, you get answers. It should be -1 plus or minus e. ln stands for natural logarithm, which is the short for log base e. There are two that you can do that. The first method is to change this in exponential form, which (x+1)^2=e^2. Now take the square root of both sides with the plus or minus sign, which is x+1=plus or minus e. Therefore p, the answer is -1 pus or minus e. The second method is to use properties of logarithms. ln(x+1)^2=2ln(abs(x+1)). Notice that there is absolute value here because when you square the answer whether it’s positive or negative, the result will still yield the positive value. Divide both sides by 2. You have ln(abs(x+1))=1. Put this is exponential form, which is abs(x+1)=e. Remove the absolute by taking plus or minus sign on the right hand side, which is x+1=plus or minus e. Therefore, the answer is -1 plus or minus e.
I’m actually gonna cry rn
ty professor jesus
what?
Last solution in comprehension section was pretty sipid. I only enjoy math when I understand it.
Done.
I don't understand the e's you put in the examples. They weren't addressed in the video. So you lost me
How can I support you at patreon sir?
Just click here and pledge what you wish! www.patreon.com/professordaveexplains
Words cant explain how you have helped me thanks so much
Thank you Dave! Our Savior!
What is the "in" please care to explain
ln is natural log, go to the tutorials earlier in the series explaining logs
Thank you didn't expected you
😮
@@ProfessorDaveExplainssir which video please 🙏 tell
I need help I need to find the answer to 5^(2x-3)=11 using ln but idk how to
Take ln of both sides, which is ln(5^(2x-3))=ln(11). Use the properties to bring the exponent down as a coefficient. (2x-3)ln(5)=ln(11). Divide both sides by ln(5) and add 3 then divide the whole answer by 2, which is (ln(11)/ln(5)+3)/2. If you want a more clear and exact answer, it would be (log_5(11)+3)/2. log_5(11) is log base 5 of 11. You can try this on your calculator if you want an approximate answer.
@@justabunga1 Why do you divide both sides by 5? I got x=(ln11+3ln5)/2ln5.
The way you've taught this is as if a person already knows certain things... If I am watching this video.... Chances are I don't know the steps that you've assumed I know.
Then go back earlier in the math series.
cood v
how about this? 4^x + 4^x+1 = 40
take log base 4!
3:17
Yoooo ! The explanations were good but then he couldn't show most of his work. You have to pause and look at his working is when get there somehow. Yooo he must just try to show his working.
4:04
Wait so you don't have to use Bhaskara? You can just stare at it?
wow
❤
❤❤❤
👍👍
math jesus
my teacher hates me
I don't show my best, I just dissapointed in others. So let them think that I'm bad, when I like making math
I left a log in my toilet
❤😂🎉😢😮😅😊
You are too fast
try setting it to 0.75 speed or even 0.5 speed
you are too slow