If log x : log y : log z = (y - z) : (z - x) | vedclass

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

Question

(B) Given $\frac{\log x}{y - z} = \frac{\log y}{z - x} = \frac{\log z}{x - y} = k$ (say).Then $\log x = k(y - z)$,$\log y = k(z - x)$,and $\log z = k(

Vedclass · Accepted Answer

$x^x \cdot y^y \cdot z^z = 1$

Vedclass · Answer

(B) Given $\frac{\log x}{y - z} = \frac{\log y}{z - x} = \frac{\log z}{x - y} = k$ (say).Then $\log x = k(y - z)$,$\log y = k(z - x)$,and $\log z = k(x - y)$.Consider the expression $x \log x + y \log y + z \log z$:$= x \cdot k(y - z) + y \cdot k(z - x) + z \cdot k(x - y)$$= k(xy - xz + yz - yx + zx - zy)$$= k(0) = 0$.Thus,$\log(x^x) + \log(y^y) + \log(z^z) = 0$.$\log(x^x \cdot y^y \cdot z^z) = \log(1)$.Therefore,$x^x \cdot y^y \cdot z^z = 1$.

Column-$I$	Column-$II$
$(1)$ Oxytocin	$(p)$ Stimulates the secretion of thyroid hormone
$(2)$ Vasopressin	$(q)$ Act on the smooth muscles
$(3)$ $FSH$ and androgens	$(r)$ Stimulates resorption of water
$(4)$ $TSH$	$(s)$ Regulate spermatogenesis

If $\log x : \log y : \log z = (y - z) : (z - x) : (x - y)$,then

Similar Questions

$A:$ Hormones are non-nutrient chemicals.
$B:$ They act as intercellular messengers and are produced in large amounts.

Select the wrong statement.

Which one of the following is the mineral for tin?

The period of oscillation of a simple pendulum of length $l$ suspended from the roof of a vehicle, which moves without friction down an inclined plane of inclination $\alpha$, is given by

Match the following:
Column-$I$ Column-$II$
$(1)$ Oxytocin $(p)$ Stimulates the secretion of thyroid hormone
$(2)$ Vasopressin $(q)$ Act on the smooth muscles
$(3)$ $FSH$ and androgens $(r)$ Stimulates resorption of water
$(4)$ $TSH$ $(s)$ Regulate spermatogenesis

Vedclass Test Series

Exam Paper Generator

Online Exam Module