Question

Solve for x:  log2(x^2-3x)=log2(5x-15).

(a) 2, 5

(b) 7

(c) 23

(d) 3, 5

I had been asked this question in an interview.

I'm obligated to ask this question of Discrete Probability topic in chapter Discrete Probability of Discrete Mathematics

Answer 1

The correct answer is (d) 3, 5

To elaborate: By using the property if logax = logay then x=y, gives 2x^2-3x=10-6x. Now, to solve the equation x^2-3x-5x+15=0 ⇒ x^2-8x+15 ⇒ x=3, x=5

For x=3:   log2(3^2-3*3) = log2(5*3-15) ⇒ true

For x=5:   log2(5^2-3*5) = log2(5*5-15) ⇒ true

The solutions to the equation are : x=3 and x=5.