Question

If 5 log 27 y + 2log 9 (81y) = 20 then what is the value of y?

Answer 1

Answer:

Convert log X base (27) to log X base (10) by below mention method.

log X base (27)= log X base(10)/log 27 base(10)

Now rewrite the given statement in this form

(logX/ log27) + ( logX / log9) + (logX/log3)= 11

(logX/ log3^3) + ( logX / log3^2) + (logX/log3)= 11

(logX/3log3) + ( logX /2log3) + (logX/log3)= 11

(1/3)*(logX/log3) +(1/2)* ( logX /log3) + (logX/log3)= 11

(logX/log3)*{(1/3)+(1/2)+1}=11

(logX/log3)*(11/6)=11

logX/log3 = 6

log X = 6*log3

Log X = log 3^6

X =3^6