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- เผยแพร่เมื่อ 28 ก.ย. 2024
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In this video I solve an exponential without calculator a calculator.
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The function in a on the LHS is an ever increasing function as it goes to infinite where a ≥ 1. The difference keeps increasing and starting at a = 1, then the LHS of the equation equals 1. We now know there is one and only one real solution to the LHS = 175.
By observation, we see that a = 4 is the one and only solution where a is greater than 1.
Why it's assumed that a is intiger? I don't recall that it was mentioned. Without this assumpton this proof is wrong.
Not really
"a" must be an integer for this problem. I forgot to mention or write in the thumbnail. Thanks for remember.
@@Geendle but isn't it implied that a is an integer by the setup given that we most likely won't get to 175 if the bases are integers?
But 'a' doesn't have to be an even number. So, we cannot resolve it as a/2 *2 in the exponent.
Elaborate
@@frax5051 this same method could not be applied to this question :
a^a - (a-1)^a = 2101
the answer is a = 5.
Prime factors of 2101 are 11, 191. But if you use the above method you can't get the answer because a is odd integer. The above method assumed a to be an even number even before finding it.
@@gontusandeep2972 I'm getting 7 tho
"a" must be an integer for this problem. I forgot to mention or write in the thumbnail. Thanks for reminding me.
@@Geendle for the above method doesn't it need to be an even integer
a = 4
Now let's see if I'm right.
It's easy and now proof that there are no other solutions
😂
Yesh! you are!
How to know 5x35 being wrong？
The factors of 175 that lead us to a positive integer solution are just 7 and 25. The others are not. Thank you.
I tried to calculate using the 5x35 and it yield different result, i was wondering how you managed to know it was 7 x 25 that has the correct answer ? Is it hit or miss or did you take the multiplication with the least difference
The factors of 175 that lead us to a positive integer solution are just 7 and 25. The others are not.
Congratulations ! What does it means? The ''factors'' of 175 that lead us to a positive integer solution are just 7 and 25. Thanks!
www.youtube.com/@user-bx8tu3sj3w, that's it! Thank you!
Terimakasih bro
Hello my friend! Thank you!
@@Geendle you are welcome
This is why i hate math.
Could I help you with somthing you don't understand well?