Consider the equation , where x is a real number log5(x - 2) = 2log25(2x - 4).
For how many different values of x does the given equation hold?
Explanation:
Given, log5(x - 2) = 2log25(2x - 4).
⇒ log5(x - 2) = 2log52(2x - 4).
⇒ log5(x - 2) = 2/2 × log5(2x - 4).
⇒ log5(x - 2) = log5(2x - 4).
⇒ x - 2 = 2x - 4
⇒ x = 2
Now, for x = 2, log5(x - 2) will not be defined. Hence, x = 2 cannot be the solution
∴ We get no solution for the given equation.
Hence, option (a).
» Your doubt will be displayed only after approval.
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.