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

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

Grade:11

3 Answers

Chetan Mandayam Nayakar
312 Points
8 years ago

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

x-3=(x-1)^2

renu akunuri
37 Points
8 years ago

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

ankitesh gupta
63 Points
8 years ago

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

 PLZ DO APPROVE THE ANSWER IF YOU LIKE IT


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