If and are three consecutive positive integers, then is:

Explanation: Since and are three consecutive positive integers, we can write them in terms of : Now, substitute these into the expression: Apply the algebraic identity : Now, take the logarithm of the expression: Using the property of logarithms : Correct Option: (d)

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NIMCET 2015 — Mathematics PYQ

NIMCET | Mathematics | 2015

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

Choose the correct answer:

Explanation

Since $x, y,$ and $z$ are three consecutive positive integers, we can write them in terms of $y$ :

$x = y - 1$

$z = y + 1$

Now, substitute these into the expression:

1 + xz = 1 + (y - 1)(y + 1)

Apply the algebraic identity $(a - b)(a + b) = a^2 - b^2$ :

1 + xz = 1 + (y^2 - 1)

1 + xz = y^2

Now, take the logarithm of the expression:

\log(1 + xz) = \log(y^2)

Using the property of logarithms $\log(a^n) = n\log a$ :

\log(y^2) = 2\log y

Correct Option: (d)

Choose the correct answer:

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