Nice Olympiad Exponential Equation: find a
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- Опубліковано 12 жов 2024
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Explore the interesting world of exponential equations with varying bases and unlock the power of exponentiation! In this educational video, we delve into the concept of exponential equations where the base is not a constant value. Learn the fundamentals, discover the properties, and master solving equations with different bases, all explained clearly and concisely. Join us on this exponential journey and level up your mathematical prowess!
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Tedius. From inspection 5^(2a) = 15. (2a) log 5 = log(15). 2a = log(15)/log(5). a = Log(15)/2*(log5)
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@@Alamaths UK.
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Thanks for the comments . Bro Adams
Каждую формулу расписал ...круто
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@@Alamaths нет, нет. Просто инженер и студент, в очередной раз
((5^a)(5^a)(5^a))/((5^a)+(5^a)+(5^a)) a=Log[25,3]+0.5=Log[5,Sqrt[15]]
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great job but you need to verify the final result
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log should be introduced at step of 5^2a = 15,you kept going back and fourth,tedious.
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………… ln(5^(2a))=ln(5•3)
(2a)ln5=ln5+ln3
2a=(ln5+ln3)/ln5
a=½(1+ln3/ln5)≈0.8413 😁
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You took a 5 line solution and turned it into minutes of algebra
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A=0,8413 ~
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Le résultat final est faux.
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Sorry, but your development around X is useless. You can use Log earlier and developp Log[sqr(15)] = 1/2 (Log3+Log5) and final result is a=1/2[Log3/Log5 + 1]
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@@Alamaths No, just an aeronautical engineer practising maths everyday to keep its 74 years old neurons alive
Why isn't 5 to the power of 2a 25?
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Если 5^(2а)=15, то
а= (log(5)3+1)/2
Что за лишние действия по замене?
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Good work
Thanks for the comments 👍
5^a•5^a•5^a = 5^(3a)
proof:
2^2•2^2•2^2
=2×2×2×2×2×2
=2^6
=2^(3×2)
5^a+5^a+5^a
3(5^a)
(5^a×5^a×5^a)/3(5^a) = 5
=> (5^a×5^a)/3=5
=> 5^(2a)/3 = 5
=> 5^(2a) = 15
=> log{5^(2a) = 15}
=> 2a log5 = log 15
=> a = 0.5(log15/log5)
=> a = 0.5(1.6826)
= 0.8413
VERIFY
(5^a×5^a×5^a)/3(5^a) =? 5
with a = 0.8413
5^0.8413 = 3.8730
3.8730^3 = 58.0939
3.8730 × 3 = 11.619
58.0939/11.619 =? 5
4.9999=❤5✔️
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[5^(a) * 5(a) * 5^(a)] / [5^(a) + 5(a) + 5^(a)] = 5 → let: x = 5^(a) → where: x > 0
[x * x * x] / [x + x + x] = 5
x³/3x = 5 → where: x > 0
x²/3 = 5
x² = 15
x = ± √15 → recall: x > 0
x = √15
5^(a) = √15
5^(a) = 15^(1/2)
Ln[5^(a)] = Ln[15^(1/2)]
a.Ln(5) = (1/2).Ln(15)
a = Ln(15) / 2.Ln(5)
a = Ln(3 * 5) / 2.Ln(5)
a = [Ln(3) + Ln(5)] / 2.Ln(5)
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Fail
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Panamá
EN VEZ DE ACERLOAS SENCILLO LO HACE MAS COMPLICADO
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If you like this video about
How to solve this math problem
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❤❤🎉🎉
Great work 👍
Thank you so much 💖, Sir.