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- เผยแพร่เมื่อ 28 ก.ย. 2024
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Find the value of x?
How to solve 27^logx+3^logx=68
In this video, we'll show you How to Solve Math Olympiad Question A Nice Exponential Equation 27^logx+3^logx=68 in a clear , fast and easy way. Whether you are a student learning basics or a professtional looking to improve your skills, this video is for you. By the end of this video, you'll have a solid understanding of how to solve math olympiad exponential equations and be able to apply these skills to a variety of problems.
#matholympiad #mathtricks #maths
27^(logx) + 3^(logx) = 68
3^(3logx) + 3^(logx) = 68
3^(logx) = u
u³ + u = 68
u³ - 64 + u - 4 = 0
(u - 4)(u² + 4u + 17) = 0
u - 4 = 0 => u = 4
3^(logx) = 4 = 3^log₃4
logx = log₃4
*x = 10^(log₃4)*
u² + 4u + 17 = 0 => no real solutions
Greate! ❤
Look at the equation. We have the sum of a number and its cube is 68.4 is obvious. No need for any explanation. The rest is trivial.
You are right, I appreciate that ❤