A Simple Problem Thats Not So Simple | A Nice Exponential Equation
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- čas přidán 11. 05. 2024
- In todays video, I will be teaching you how to solve an interesting problem. Make sure to like, subscribe, and also comment any questions or video ideas you may have relating to math!
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8 = 2^3 and 32 = 2^5, so the initial equation can be rewritten as (2^3)^x = 2^5
By the properties of powers, (2^3)^x = 2^3x and the equation becomes 2^3x = 2^5
The bases are the same, so the exponents must be the same too, hence 3x = 5
And so x = 5/3
Seems simpler this way 🙂
Way simpler lol. He made it so much more complicated than necessary
Oh wait, I just realized he showed that method at the end😅
@@Yarkz. Oh, I missed that. I stopped watching when he was checking that x = 5/3 was indeed the correct answer.
Doh! 😅
Yep . .. that's the way I would have done it too. No need for logs in this case.
Much simpler than using logarithms. Plus it, affords good practice in solving exponential equations.
In the UK, 5/3 is regarded as an 'improper fraction' and is therefore NOT the correct final answer, but should be reduced to 1 2/3 (one and two-thirds).
Yes 5/3 = 1+2/3. However, for power indices, 5/3 is the better form. If you need to do further calculations based on a result, you will need to use the 5/3 form. Indeed I have yet to see Maths books that do not favour this form - so the answer in the video is preferential.
I am from the UK. I have never had a teacher who expressed indices a whole number + a fraction - neither have I ever seen it in a text book. There is a logical reason for preferring the improper fraction form of exponentials. Analytically, raising 8 to the power of 5/3 means the cube root of 8, which is 2, is raised to the power of 5, which is 32. This is why I was able to solve the equation in my head - so there is good reason not to get rid of the improper form. Raising 8 to power 1+2/3 or 1.6667 tells you no more than 8 is raised to that power.
I was able to solve the equation in my head because 8 to the power of 5/3 means the cube root of 8, which is 2, is raised to the power of 5, which is 32.
Зачем усложнять решение, логорифмы здесь не нужны, достаточно привести к одному основанию и будет 3x=5
It also helps if you use log base 2.
5/3
2^(3x) = 2⁵
*x = 5/3* = 1 + 2/3
8 elv x = 32 ?
Como 8 = 2 elv 3 e
32 = 2 elv 5, vem:
(2 elv 3 ) elv x = 2 elv 5
2 elv 3x = 2 elv 5, como as bases (2) são iguais
podemos corta-las e
3 x = 5 e x = 5/3.
Why is this simple problem stated to be difficult?
(2^3)^x = 2^5
X = 5/3 = 1.6667
sloppy - you need to edit out confusing mistakes
This guy made the solution way more complicated than necessary!
Man kann es auch unnötig kompliziert machen. Wofür hier log?
Самое дурацкое решение.