USA Olympiad Exponential Equation | Solve for a..?

USA Olympiad Exponential Equation | Solve for a..? #exponentialequation #maths #math

[@假老二]

Annwer ln10/3ln5 is more directly

[@RealQinnMalloryu4]

125 10^105^5 2^52^5^1^1 1^1^2^1 2^1 (a ➖ 2a+1). 10 2^5 (a ➖ 5a+2).

[@meshulamoren8633]

3×5^a=10 5^a=10/3 a=(log10-log3)÷(log5) a=0.7481

[@prollysine]

3*5^a=10 , a=log10/(3*log5) , test , 5^(log10/(3*log5)) * 5^(log10/(3*log5)) * 5^(log10/(3*log5)) =10 , OK ,