Japanese | Math Olympiad Exponent Equation | A Nice Algebra Problem 👇👇👇 | Solve 10^x+100^x=1000^x

[@BruceLee-io9by]

Great algebraic exercise.

[@superacademy247]

Yes, thanks

[@benyseus6325]

X = log(phi). Golden ratio

[@SidneiMV]

first divide by 10ˣ
1 + 10ˣ = 100ˣ
10ˣ = u > 0
u² - u - 1 = 0
u = 10ˣ = (1 + √5)/2
*x = log(1 + √5) - log2*

[@sergiya1934]

you lost one possible solution, u=0; does not matter in this case, but in general it is not accurate.

[@SidneiMV]

@@sergiya1934 variable u = 10ˣ so the variable u cannot be equal to zero