If x, y, z are in geometric progression and a | vedclass

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

Question

(C) Since $x, y, z$ are in geometric progression,we have $y^2 = xz$. Let $a^x = b^y = c^z = \lambda$. Taking log on both sides,we get $x \log a = y \l

Vedclass · Accepted Answer

$log_b\ a = log_c\ b$

Vedclass · Answer

(C) Since $x, y, z$ are in geometric progression,we have $y^2 = xz$. Let $a^x = b^y = c^z = \lambda$. Taking log on both sides,we get $x \log a = y \log b = z \log c = \log \lambda$. Thus,$x = \frac{\log \lambda}{\log a}$,$y = \frac{\log \lambda}{\log b}$,and $z = \frac{\log \lambda}{\log c}$. Substituting these values into $y^2 = xz$,we get: $(\frac{\log \lambda}{\log b})^2 = (\frac{\log \lambda}{\log a}) 	imes (\frac{\log \lambda}{\log c})$. This simplifies to $(\log b)^2 = \log a \cdot \log c$. Dividing both sides by $\log a \cdot \log b$,we get $\frac{\log b}{\log a} = \frac{\log c}{\log b}$,which implies $\log_a b = \log_b c$. Taking the reciprocal,we get $\frac{1}{\log_a b} = \frac{1}{\log_b c}$,which is $\log_b a = \log_c b$.

If $x, y, z$ are in geometric progression and $a^x = b^y = c^z$,then . . . . . .

Similar Questions

If the roots of the equation $x^5-40x^4-Px^3-Rx-S=0$ are in geometric progression and the sum of the reciprocals of the roots is $10$,then $|S|=$

If $5, 5r, 5r^2$ are the lengths of the sides of a triangle,then $r$ cannot be equal to

Let $S$ be the sum,$P$ the product,and $R$ the sum of reciprocals of $n$ terms in a $G.P.$ Prove that $P^{2} R^{n} = S^{n}$.

If ${x_1}, {x_2}, {x_3}$ as well as ${y_1}, {y_2}, {y_3}$ are in $G$.$P$. with the same common ratio,then the points $({x_1}, {y_1}), ({x_2}, {y_2})$ and $({x_3}, {y_3})$:

The first two terms of a geometric progression add up to $12$. The sum of the third and the fourth terms is $48$. If the terms of the geometric progression are alternately positive and negative,then the first term is

Vedclass Test Series

Exam Paper Generator

Online Exam Module