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Question

The set  is equal to

Solution

Correct option is

[1/5, )

If log1/5 x ≤ 1 i.e. x ≥ 1/5 then the give equality reduces to

1 – log1/5 x + 2 = 3 – log1/5 x which is trivially true. If 1 < log1/5 x ≤ 3 then the given equality becomes log1/5 x – 1 + 2 = 3 – log1/5 x 

⇒ 2log1/5­ x = 2⇒ log1/5 x = 1 which is not true.

Also if log1/5 x – 3 than the given equality reduces to log1/5 x – 1 + 2 = log1/5 x – 3 which clearly is not true.

Hence the required set is equal to [1/5, ∞].

SIMILAR QUESTIONS

Q1

The set of all x satisfying the equation 

Q2

The set of all solutions of the inequality  contains the sets

Q3

The set of all the solutions of the inequality 

           

Q4

If log3 x + log3 y = 2 + log3 2 and log3 (x + y) = 2 then

Q5

The set of all solutions of the equation 

 

                                                                                           

Q6

 then the value of log30 8

Q7

 then the value of ab + 5(a – b) is

Q9

The set of all values of x satisfying 

           

Q10

The set of  is equal to