Sweden | A Nice Algebra Problem | Math Olympiad👇

Sweden | A Nice Algebra Problem | Math Olympiad👇
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Find the value of x?
How to solve (-5^x)= 5
In this video, we'll show you How to Solve Math Olympiad Question A Nice Exponential Equation (-5^x) = 5 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.
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[satrajitghosh]

( - 5 ) ^ ( x - 1) = - 1
x = 1 + log ( -1)/ log ( -5)
= 1 + 1 /.( 1 + log (5) / log (-1))
= 1 + 1/( 1 + log ( 5) / (i π))

[jackskids]

I see 9 comments complementing this solution, however this is not the correct or complete solution, since it is in terms of log(i). Now log(i) is any odd integer multiple of i. pi. The correct solution is 2(n+1) pi - i log 5) / (pi - i log 5) for all integers n.

[skiqu]

Why not just do x=2/2? (-5)(-5)=25, sqrt 25= 5

[walterwen]

Sweden Math Olympiad: (– 5)ˣ = 5; x =?
If: aˣ = b, log(aˣ) = logb; x = loga/logb
For logarithmic math applications, a, b ϵ R⁺; No negative, complex or imaginary number
5ˣ > 0, (– 5)ˣ < 0, (– 5)ˣ < 5; No rational solution for this irrational exponential equation.

[borisjeud]

● (-5)x=5
Super theorem!
Well explained