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3^a(1+3+9)=843^a=84/133^a=4a log3=log 4a=log4/log3-=1.262
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)/2For x=4, a=ln4/ln3=1.26186... For x=(-5±i√59)/2, we'll leave that as an exercise for the more energetic.
I'm glad you followed along with the solution!
so 3^a=4log_3(4)=a
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
thanks for your response
@@rashel1 Thanks!
too slow
I hate the way you wrote "2", it is beyond Ugly!
3^a(1+3+9)=84
3^a=84/13
3^a=4
a log3=log 4
a=log4/log3-=1.262
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.
I'm glad you followed along with the solution!
so 3^a=4
log_3(4)=a
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
thanks for your response
@@rashel1 Thanks!
too slow
I hate the way you wrote "2", it is beyond Ugly!