Question Number 113996 by Aina Samuel Temidayo last updated on 16/Sep/20

Commented byMJS_new last updated on 16/Sep/20

((ln ((81)/8))/(2ln (9/2)))=((ln (√((81)/8)))/(ln (9/2)))=((ln (9/( (√8))))/(ln (9/2)))=log_(9/2) (9/( (√8)))

Answered by bobhans last updated on 17/Sep/20

9^x +(1/3).9^x  = 2(√2) .2^x +(√2).2^x   ⇒(4/3).9^x  = 3(√2).2^x   ⇒9^(x−1)  = 2^(x−(3/2))  ; (x−1)ln (9)=(x−(3/2))ln (2)  xln 9−xln 2 = ln 9−(3/2)ln 2  x.ln ((9/2)) = ln ((9/(2(√2)))) ⇒ x= log _(9/2) ((9/( (√8))))