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

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

Answer»

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

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