If x, y, z are three consecutive positive integers, then log (1 + xz) is

Question

Question

This question was previously asked in

NIMCET 2015 Official Paper

Answer 1

Concept:

Logarithm Rule

log mⁿ= n log m

Calculations:

Let x, y, z are three consecutive positive integers.

⇒ y = x + 1 and z = y + 1

⇒ z = x + 2

Consider, log (1 + xz)

= log [1 + x(x+2)]

= log [1 + x²+ 2x]

= log (1 + x)²

= 2 log (1 + x)

= 2 log y

Hence, If x, y, z are three consecutive positive integers, then log (1 + xz) is 2 log y