Question

x=log3 y=log6
determine log27 in terms x and y

Answer 1

If logx (base 27) +logx (base 9) +logx (base3) =11 then find the value of x?

It's time to give your home a character with Gyproc!

Dibyaranjan Senapati

Answered 5 years ago

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