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

The $4^{\text{th}}$ term of a $GP$ is $500$ and its common ratio is $\frac{1}{m}$,where $m \in N$. Let $S_n$ denote the sum of the first $n$ terms of this $GP$. If $S_6 > S_5+1$ and $S_7 < S_6+\frac{1}{2}$,then the number of possible values of $m$ is $..........$

The roots of the equation $x^5 - 40x^4 + px^3 + qx^2 + rx + s = 0$ are in $G.P.$ The sum of their reciprocals is $10$. Then the value of $|s|$ is

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 the roots of the equation $8 x^3+6 p x^2+3 q x-27=0$ are in a geometric progression,then $q^2+9 p^2+6 p q+q/p=$

If the sum of three terms of a $G.P.$ is $19$ and their product is $216$,then the common ratio of the series is

Vedclass Test Series

Exam Paper Generator

Online Exam Module