Germany | Can You Solve This? | Math Olympiad Exponential Problem | Best TricK... 

X= 1.

same funds , 5^(ln3/ln5)x * 5^x^2 = 5^(ln15/5) , (ln3/ln5)x + x^2 = (ln15/5) , x= 1 , -1.68261 , test x=1 , 3^1 * 5^1 =3*5 , 3*5=15 , same , OK , test x= -1.68261 , 3^(-1.68261)*5^((-1.68261)^2)=14.9999... ~ 15 , OK ,

Yes, or ... 3^x·5^(x^2) = 15 notes: • log₅(3) = 0,682606 • log₅(15) = 0,682606 5^(0.682606x)·5^(x^2) = 5^1,682606 5^(0.682606x + x^2) = 5^1,682606 same base (= 5) => 0.682606x + x^2 = 1,682606 x^2 + 0.682606x - 1,682606 = 0 Δ = 0.682606² - 4·1·(-1.682606) = 7.196374 √7.196374 = ±2.682605 • root #1: x = (-0.682606 + 2.682605)/(2·1) = 0.99999 = 1 • root #2: x = (-0.682606 - 2.682605)/(2·1) = -1.682605 ----- final results ----- ■ x = 1 ■ x = -1.682605 🙂