a great exponential equation | exam preparation
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- เผยแพร่เมื่อ 1 ก.ค. 2024
- You should know these rules.
If you're reading this ❤️. What do you think about this problem?
Hello My Friend ! Welcome to my channel. I really appreciate it!
@higher_mathematics
#maths #math
mildly overpcomplicated, just take ln of both sides and express x. done.
As usual. Fake math channel doing fake math.
Well not everyone starts up as legends, it takes time to get there.
@@HoSza1 what do you mean? "Becoming a legend" has nothing to do with this conversation. It is true that not everyone starts up as legends. But a channel like this one will NEVER become a legend. Man, this is the same as channels with questions like
"1ⁿ+2²ⁿ=2ⁿ Olympiad Question, 99% FAIL"
They are fake channels. There are fake channels about food, about nature, about life hacks, etc. And there are fake channels about Math. Did you never realise that? Such channels don't want to become legends. They just want to try to make money, most fail, but they keep on popping. They are scams. They don't want to teach, to inform, to do a good job. Get real. Do you really think a youtuber with a Math channel wanting to learn and teach Math would solve a question like
2^x = 7^{x+2}
in such way he did in the video??? Do you really have such bad opinion about him??? Search and you will find even worse videos. For example, an example I never forget, a old teacher, probably false information, solving
2^x+2^y+2^z = 49
or something like that. Do you know how he solves that? Search and see. Man, it is insane. A simple question, not even phrased properly, because the question should say
find x,y,z natural numbers such that ...
that is just binary representation of a number, so it is solved by a normal person with
49 = 32+16+1
= 2⁵+2⁴+2⁰
the old teacher solves in a nonsensical way. Why? Because he has a fake Math channel.
Love your series, what books would you recommend to someone looking to compete in olympiads?
Yes !!! Or ...
2^x = 7^(x + 2)
note: log₇(2) = 0.356207
(7^0.356207)^x = 7^(x + 2)
7^(0.356207x) = 7^(x + 2)
same base (= 7)
0.356207x = x + 2
0.356207x - x = 2
-0.643793x = 2
x = 2/-0.643793
■ x ≈ -3.106588
🙂
Why so complicated?
2^x = 7^(x+2)
x log(2) = (x+2) log(7)
x (log(7) - log(2)) = -2 log(7)
x = - 2 log(7) / (log(7) - log(2))
x = 2 log(7) / (log(2) - log(7))
x = 2 log(7) / log(2/7)
2^k=7 , k=ln7/ln2 , 2^x=2^((ln7/ln2)(x+2)) , x*ln2=((ln7/ln2)(x+2))*ln2 , x=((ln7/ln2)(x+2)) , x(1-ln7/ln2)=2*ln7/ln2 ,
x=(2*ln7/ln2)/(1-ln7/ln2) , x=~ -3.10659 , test , 2^(-3.10659)=~ 0.116098 , 7^(-3.10659+2)=0.116098 , same , OK ,
-14/5