Canada|Olympiad Math Exponential Equation|what is the value of X ❓

[@tojimahamatxudayberganov]

😂😅❤

[@orionpritchard1117]

I think it's easier to divide by 10^x instead of 1000^x:
10^x + 100^x = 1000^x Divide by 10^x
1 + 10^x = 100^x Set s = 10^x
1 + s = s^2 Setup for factoring
s^2 - s - 1 = 0 Quadratic Formula
s = (1 +/- sqrt(1 + 4)) / 2 Take positive factor
s = (1 + sqrt(5)) / 2 Solve for x
x = log10(0.5 + sqrt(5) / 2)

[@grenouille1001]

exactly

[@Koushiro-blmegtm]

X = -log((√5 - 1)/2)

[@hugovdm3323]

X es el logaritmo de fi ( número de oro)