USA Olympiad Exponential Equation: find k!

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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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[Alamaths]

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[jan-willemreens]

... Good day to you math friend, I saw a well explained math problem, and wishing you a prosperous continuation of your channel ... greetings from The Netherlands, Jan-W

[walterwen]

2(5^k) = 100, 5^k = 50 = 2(5^2), 5^(k - 2) = 2, k - 2 = log2/log5 = 0.431, k = 2.431

[cyruschang]

5^k + 5^k = 2(5^k) = 100
5^k = 100/2 = 50
klog5 = log50 = 1 + log5
x = 1 + 1/log5

[mystericals]

Dont know maths that well, just guest the answer as 2.4xx which results in 2^2.4xx = 50, 50+50=100😅

[RyanLewis-Johnson-wqxs]

Input
5^(log(5, 2) + 2) + 5^(log(5, 2) + 2) = 100
Result
True
Expanded logarithmic form
True x=log[5, 2]+2 final answer