Question #385ef

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Answer 1 · 2018-01-11T08:41:28

#log_x3 log_(x/81) 3 = log_(x/729)3 #

#=>log_x3 log_(x/81) 3 = log_(x/729)3 #

#=>log_x3 = log_(x/729)/ log_(x/81) 3#

#=>log_x3 = log_3(x/81) /log_ 3(x/729)#

#=>log_x3 = (log_3x-log_3 3^4) /(log_ 3x-log_3 3^6)#

#=>log_x3 = (log_3x-4log_3 3) /(log_ 3x-6log_3 3)#

#=>1/log_ 3x = (log_3x-4) /(log_ 3x-6)#

Taking #log_x3=y#

#=>1/y = (y-4) /(y-6)#

#=>y^2-4y = y-6 #

#=>y^2-5y +6=0 #

#=>y^2-3y-2y +6=0 #

#=>y(y-3)-2(y -3)=0 #

#=>(y-3)(y-2)=0 #

So #y=2 and y=3#

When #y=2#

#log_x3=2=>x^2=3=>x=3^(1/2)#

When #y=3#

#log_x3=3=>x^3=3=>x=3^(1/3)#