logbase4(x-1)=logbase2(x-3) have how many sloutions

logbase4(x-1)=logbase2(x-3)

x-3=(x-1)^2

1/2log(x-1) = log(x-3)    " here now both sides of equations has same base that is 2"

log (x-1)^1/2 =log (x-3)   "now we can eliminate the log on both side because they have same base "

(x-1)^1/2       =(x-3)

x-1= (x-3)²

x²-7x+10=0

therefore x=2,5

THIS EQUATION WILL HAVE 2 REAL AND DISTINCT SOLUTIONS

 log₄(x-1)= log₂(x-3)

 ON SOLVING   [log(x-1)/log4] = [ log(x-3)/log2]

                  [log(x-1)/2log2] = [log(x-3)/log2]

                    CANCELLING LOG2 BOTH SIDES WE GET

                   log(x-1)= 2 log (x-3)

                   log(x-1) = log(x-3)² 

     TAKING ANTILOGS BOTH SIDES WE GET

     (x-1)=(x-3)²

    ON SOLVING THE QUADRATIC IN x YOU WILL GET TWO REAL AND DISTINCT VALUES WHICH IS 5,2 

   HOPE THIS HELPS

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