Solving a basic exponential equation 8^x=4 (you don’t need logarithm)

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How to solve this exponential equation 8^x=4? A usual strategy is to write both sides with a common base, and then make the exponents equal to each other. This question is from Instagram: www.instagram....
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Опубликовано:

28 сен 2024

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Комментарии : 84

@bprpmathbasics 6 месяцев назад

How do I find x: 2^(x-5)=3^(x+1) Answer here: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-vitK9oR8nkc.html

@DotRabbit 6 месяцев назад

Approximately it is x ≈ -11.25706

@rustler08 6 месяцев назад

This is why it's important to memorize this as part of the exponent rules. You should know that x^1/2 is a different way of writing "square root", which would immediately let you know it's wrong and eliminates a choice.

@Hydratz 6 месяцев назад

I forgot about the math but I thought of it as 2*2*2 is 8 and 2*2 is 4 so basically 8 to the "2/3" (because you used 2 of the 3 2's) is 4

@jacobgarcia9761 6 месяцев назад

@bprp explain why this is a good way or a bad way of thinking

@Trumpetis1 6 месяцев назад

So in the form x^(y/z), if the z root of x is a whole number, then the y power of it is the solution. That is the mathematical way of explaining your method. Since the cube root of 8 is 2 (whole number) just square that and its 4. This is the equation bprp uses in the video. You basically simplified it to an easier to understand form.

@Hydratz 6 месяцев назад

@@Trumpetis1 Nice

@rustler08 6 месяцев назад

@@jacobgarcia9761Does the explanation work for other problems? If it doesn't, it's a bad way of thinking.

@Viki13 6 месяцев назад

This works cuz it's all integers I don't think this would work for non integer problems

@ZipplyZane 6 месяцев назад

When you posted this, I actually did it with logs before I actually stopped to think about it.

@Fibok69 6 месяцев назад

4/3

@sakibeditz6236 6 месяцев назад

I solved it on my own and I am now proud of myself... xD

@nexoy5457 6 месяцев назад

x=4/3

@kishanbandshamsabad217 4 месяца назад

4/3

@lerarosalene 6 месяцев назад

Isn't exponential function one-to-one if and only if base isn't equal to 0 or ±1?

@bugsfudd8295 6 месяцев назад

You want to be careful raising to the power before doing the root - -8^(2/3) is -8

@wyffd 6 месяцев назад

log base 8 entered the chat

@darranrowe174 6 месяцев назад

Yes, I immediately thought of log a^n = n log a too. But I guess that doesn't give you a nice easy to read off result. This would leave you with x = log_8(4).

@funwithmadness 6 месяцев назад

I was never particularly good at math. Now, I've been reduced to idiot level.

@MichelleyB-zk3eh 6 месяцев назад

Lost me at the check

@Nikioko 6 месяцев назад

2^3x = 2² 3x = 2 x = 2/3

@sarak8576 6 месяцев назад

27^3/4 =81

@DotRabbit 6 месяцев назад

27^x = 81 then 3^3x = 3^4 well now we can equate powers which means 3x=4 then x= 4/3 we can check it by putting 4/3 in the place of x. 27^4/3 = (cube root 27)^4 = 3^4 = 81

@ahmet00fx 6 месяцев назад

People before logarithm.

@lawrencejelsma8118 6 месяцев назад

People wanting to make the solution more lengthy 😂🤣 Since taking a logarithm of any base on both sides isn't taking a logarithm of a negative value nor a 0 it is okay to think of logarithm on both sides. Then log (2^3) dividing into log (2^2) is 2/3 in any log base to separate from x in xlog(2^3)=log(2^2)

@bijipeter1471 6 месяцев назад

Thank you, sir x=4/3

@touristofmeshes4425 6 месяцев назад

im thankful i remember b^y=x and log_b(x)=y from one of my high school math teachers a while back I knew automatically it was 2/3

@DonTheRealMan 6 месяцев назад

Is it just je or were those police sirens blaring in the background at 2:55 ?

@richardl6751 6 месяцев назад

Police, fire or ambulance.

@v1nzaro 6 месяцев назад

4/3😁

@pythondrink 4 месяца назад

How did you get liked?

@0ned 6 месяцев назад

Not even slightly convoluted! Thanks for a clear explanation of exponential 1:1 function!

@liambyrne591 6 месяцев назад

What is this about

@g.4279 6 месяцев назад

log_8(4) of course

@StephenMarkTurner 6 месяцев назад

I took advantage of the multiple guess. Cube root of 8 = 2, then squared = 4.

@sameersmith2005 6 месяцев назад

1. xlog8 = log4 ( By taking log both sides ) 2. xlog(2)^3 = log(2)^2 3. 3xlog2 = 2log2 4. 3x = 2 5. x = 2/3

@Robi2009 6 месяцев назад

"many students would say x=1/2" ? How? 8^1/2 is the same as sqrt(8) and 4 is sqrt(16)... Sqrt (8) is ca. 2,8

@spartanhawk7637 6 месяцев назад

As someonw who graduated a few years ago, seriously can't thank you enough for making these videos. They really help me keep my skills sharp.

@JubeiKibagamiFez 6 месяцев назад

I went to my calc... I couldn't think of what number and power equals 81 other than 9².

@m.h.6470 6 месяцев назад

Solution: 8ˣ = 4 (2³)ˣ = 2² 2³ˣ = 2² |log₂ 3x = 2 |:3 x = 2/3 Test: ³√(8²) = 4 ³√64 = 4 ³√(16 * 4) = 4 ³√(4 * 4 * 4) = 4 ³√(4³) = 4 4 = 4

@florianbasier 6 месяцев назад

a bit unprecise in your explanations. a^b = a^c b=c is only true if a is not in {-1;0;1}

@s.7980 5 месяцев назад

Thanks for your clear and concise teaching! More people need to watch this.

@askemadsen21 6 месяцев назад

27^x = 81 (3^3)^x = 3^4 3^3x = 3^4 3x = 4 x = 4/3 check: 27^4/3 = (3√27)^4 = 3^4 = 81

@williamsquires3070 6 месяцев назад

The simplest way is to just try all four possible answers. 😊

@iamcodephilic 3 месяца назад

The answer for the last question will be (4/3)

@teelo12000 6 месяцев назад

Your explanation for why we can simplify 2^3x = 2^2 is too complicated, imo. Just say "take log base 2 on both sides".

@amininja 6 месяцев назад

Pretty sure this video was made with the assumption that the viewers lacked knowledge about logarithm

@gta4everrr 6 месяцев назад

27^x = 81 9^(3/2)^x = 9^2 9^[(3/2)x] = 9^2 (3/2)x = 2 x = 4 / 3

@kyokazuto 6 месяцев назад

How do you get the base when you don't have it memorized. I saw from the comments its 3 but I wouldn't know that otherwise.. is there any way to calculate it..

@monke7566 6 месяцев назад

yes, you find the prime factors of the number, first do 8/2= 4 then do 4/2=2 then do 2/2=1, you used 3 2's, so you do 2³=8

@commandingangel 6 месяцев назад

How do we solve? Wolfram Alpha

@robinsparrow1618 6 месяцев назад

x=4/3 for the question at the end

@ngyuzhemoe7107 6 месяцев назад

I used logs

@z000ey 4 месяца назад

DROP THE BASE :)

@timturner7609 6 месяцев назад

Its x=3/4 right?

@gohanks34 6 месяцев назад

lol i definitely did this the more complicated way: ln (8^x) = ln (4) x ln (8) = ln (4) x = ln (4) / ln (8) plugging into a calculator gives you x = 2/3

@Yewtewba 6 месяцев назад

You don't need a calculator if you use log with base 2. You can use any base you want.

@ianjlilly 6 месяцев назад

Take logs base 2!

@robinsparrow1618 6 месяцев назад

this is true because 2!=2

@shivnathbanerjee5868 6 месяцев назад

X = 4/3

@kushW_24 6 месяцев назад

X=4/3

@Tinwoodie100 6 месяцев назад

X=4/3

@Foxekins 6 месяцев назад

x = 4/3

@AndRe-nz7mc 6 месяцев назад

4/3

@ZackBlackwood97 6 месяцев назад

I attempted the end question, and got a totally different answer than the comments. Someone help. NEVERMIND. I realised the mistake

@herlanggaizul6965 6 месяцев назад

For me, I just use logarithm 😂 8^x = 4 X = (8)log(4) X = (2³)log(2²) X = 2/3 (2)log(2)

@demne2300 6 месяцев назад

this question is pretty normal question when i learned logarithm at 11th grade

@Rachit1008 6 месяцев назад

8^x=4 (2^3)^x=2^2 2^3x=2^2 Therefore 3x=2 and x=2/3. This is right solution..

@staremperor8741 6 месяцев назад

I actually did a trial and error with the check method before watching the video for finding the answer lol

@jacobgarcia9761 6 месяцев назад

I meant 4/3

@vvvkrant5339 6 месяцев назад

@@jacobgarcia9761 wow

@sylvio1687 6 месяцев назад

It's very easy i havent watched the video yet but 8 is 2^3, and 4 is 2^2 so we can say 3X=2, so X= 2/3 Edit the other problem 27^X= 81. We can rewrite as 3^3X = 3^4 so 3X=4 so X=4/3