If x, y, z are in H.P.,then the value of the | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given that $x, y, z$ are in $H.P.$,we have $y = \frac{2xz}{x + z}$.Consider the expression $E = \log(x + z) + \log(x - 2y + z)$.Using the property

Vedclass · Accepted Answer

$2\log(x - z)$

Vedclass · Answer

(B) Given that $x, y, z$ are in $H.P.$,we have $y = \frac{2xz}{x + z}$.Consider the expression $E = \log(x + z) + \log(x - 2y + z)$.Using the property $\log(a) + \log(b) = \log(ab)$,we get $E = \log((x + z)(x - 2y + z))$.Substitute $y = \frac{2xz}{x + z}$ into the expression:$E = \log\left((x + z)\left(x + z - 2\left(\frac{2xz}{x + z}\right)\right)\right)$$E = \log\left((x + z)\left(x + z - \frac{4xz}{x + z}\right)\right)$$E = \log\left((x + z)^2 - 4xz\right)$$E = \log(x^2 + 2xz + z^2 - 4xz) = \log(x^2 - 2xz + z^2)$$E = \log((x - z)^2) = 2\log(x - z)$.

If $x, y, z$ are in $H.P.$,then the value of the expression $\log(x + z) + \log(x - 2y + z)$ is

Similar Questions

Find the harmonic mean of $a/b$ and $b/a$.

If $\log (x + z) + \log (x + z - 2y) = 2\log (x - z),$ then $x, y, z$ are in

If the $5^{th}$ term of a $H.P.$ is $\frac{1}{45}$ and the $11^{th}$ term is $\frac{1}{69}$,then its $16^{th}$ term will be:

If $\frac{x + y}{2}, y, \frac{y + z}{2}$ are in $H.P.$,then $x, y, z$ are in

If $\frac{1}{b + c}, \frac{1}{c + a}, \frac{1}{a + b}$ are in Arithmetic Progression $(AP)$,then $a^2, b^2, c^2$ are in which progression?

Vedclass Test Series

Exam Paper Generator

Online Exam Module