Harvard Elementary High School maths question | Find the value of a=?

[@Dbaby52]

3^a(1+3+9)=84 3^a=84/13 3^a=4 a log3=log 4 a=log4/log3-=1.262

[@wes9627]

Substitute x=3^a: x^3+x^2+x-84=0 has root x=4. Divide by (x-4): x^2+5x+21=0. x=(-5±i√59)/2 For x=4, a=ln4/ln3=1.26186... For x=(-5±i√59)/2, we'll leave that as an exercise for the more energetic.

[@rashel1]

I'm glad you followed along with the solution!

[@davidseed2939]

so 3^a=4 log_3(4)=a

[@prollysine]

let u=3^a , u^3+u^2+u-84=0 , (u-4)(u^2+5u+21)=0 , u=4 , 3^a=4 , a=log4/log3 , test , 3^a+9^a+27^a=4+16+64 , --> 84 , OK , 1 -4 solu , a=log4/log3 , 5 -20 21 -84

[@rashel1]

thanks for your response

[@prollysine]

@@rashel1 Thanks!

[@joanchan8638]

too slow

[@wmhuang]

I hate the way you wrote "2", it is beyond Ugly!