USA Nice Olympiad Exponential Equation | Solve for X

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[@RyanLewis-Johnson-wq6xs]

5^x*5^x*5^x=10 x=Log[125,2]+1/3=Log[125,2]+0.3 recurring=(1+Log[5,2])/3=Log[5,Surd[2,3]]+0.3 recurring

[@Sci-Marvels]

Interesting approach! It’s always fascinating to see different methods to solve these kinds of equations. Thanks for sharing your solution!

[@KUS-2024]

5^(3X)=10 3X×log(5)=log(10)=1 X×log(5)=1/3 X=1/(3×log(5))

[@abardi2142]

x=1/(3*Log5)

[@user-et4ji4gj7k]

10/21 is also right

[@mayaq8324]

Using my calculator I can confirm that 10 = 10

[@miracbarsapaydn650]

X =log(5)[10] / 3

[@TheTinkywinky3]

Olympiad??? Are you kidding? I could solve it in mind, and you don't need therefor over 6 Min.

[@Mike--K]

I must be missing something very important because this did not appear to be a difficult problem. (5^x)( 5^x)(5^x) = 10 can be written as (5 * 5 * 5)^x = 10, or 125^x = 10. Taking the log of both sides gives xlog(125) = log(10). Since log(10) = 1, the equation can be written as xlog(125) = 1. Divide both sides by log(125) and the equation can be written as x = 1/log(125).

[@balanbalan82]

the answer is coming as 1 not 10

[@balanbalan82]

i used the cal

[@Sci-Marvels]

You're absolutely correct! Simplifying the equation in this way makes it much more straightforward. It's great to see how different approaches can lead to the same result. Thanks for breaking it down so clearly! 👍

[@its_anonymous490]

Put x=2/3 and see the equation satisfy

[@user-wk6je7pi4h]

5^1.432=10

[@ibrahimbaig-ro1tp]

x is 0.96/2

[@cn_minijacob3046]

Is this really usa's olympiad math level ?

[@NEELUSINGH-gn9jg]

Hello dear sir

[@RojiDevi-y5r]

Hi

[@Anushka2470]

😂 even 8 standard kid can solve this

[@adityatiwariofficials]

Log is introduced in class 8 huuhhh...?