What is x if #log_3 (x-1) + log_3 (x-9) = 2#?

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Answer 1 · 2018-04-04T18:36:27

#x=10#

We know that ,

#color(blue)((1)log_aM+log_aN=log_a(MN)#

#color(blue)((2)log_aX=n<=>X=a^n#

Here,

#log_3(x-1)+log_3(x-9)=2...toApply (1)#

#=>log_3((x-1)(x-9))=2...toApply (2)#

#=>(x-1)(x-9)=3^2#

#=>x^2-x-9x+9=9#

#=>x^2-10x=0#

#=>x(x-10)=0#

#=>x=0 or x-10=0#

#=>x=0 or x=10#

But, #x=0=>x-1=0-1=-1 < 0#

# and x-9=0-9=-9 < 0#

So,#x!=0#

i.e. #x=10#