USA Olympiad Exponential Equation: solve for a=?

USA Olympiad Exponential Equation: solve for a=?

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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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[ajitandyokothakur]

You do not need to split log(10) as log(2x5) = log2 + log5 because log10 = 1. then your final solution is: a = (1/3)(1+1/log2). Dr. Ajit Thakur (USA).

[Alamaths]

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[keeteo]

quicker to write the equation as 2^(3a)=2*10 Then divide both sides by 2 to get 2^(3a-1)=10 so (3a-1)log(2)=1 ...

[RyanLewis-Johnson-wqxs]

2^a*2^a*2^a=20 2^(Log[8, 1.25]+1.3 recurring)* 2^(Log[8, 1.25]+1.3 recurring)* 2^(Log[8, 1.25]+1.3 recurring)=20 a= Log[8, 1.25]+1.3 recurring=(Log[2, 5]+2)/3 It’s in my head.

[Howiefm]

This is an Olympiad question? Seriously 😢 … oh it’s USA math Olympiad … that explains it 😅