(A) Let the three numbers be $a, b,$ and $c$ in a geometric progression.$\therefore b^2 = ac$Taking the logarithm on both sides,we get:$\log(b^2) = \l

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(A) Let the three numbers be $a, b,$ and $c$ in a geometric progression.$\therefore b^2 = ac$Taking the logarithm on both sides,we get:$\log(b^2) = \log(ac)$$2 \log b = \log a + \log c$$\log b = \frac{\log a + \log c}{2}$This condition shows that the logarithms $\log a, \log b,$ and $\log c$ satisfy the property of an arithmetic progression.

Class 11 Mathematics Sequences and Series Geometric progression

Medium

If three numbers are in a geometric progression,then their logarithms are in:

A
Arithmetic progression.
B
Geometric progression.
C
Harmonic progression.
D
None of these.

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Class 11 Questions

Class 11

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Chapter

Sequences and Series

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Geometric progression

If the roots of the equation $8x^3 - 14x^2 + 7x - 1 = 0$ are in $G.P.$,then the roots are

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If the first term of an infinite geometric series is $1$ and each term is equal to the sum of all the terms that follow it,then what is its fourth term?

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

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If the $4^{th}$,$7^{th}$,and $10^{th}$ terms of a Geometric Progression $(GP)$ are $a, b,$ and $c$ respectively,then:

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The first term of an infinite geometric progression is $x$ and its sum is $5$. Then:

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If three numbers are in a geometric progression,then their logarithms are in:

Similar Questions

If the roots of the equation $8x^3 - 14x^2 + 7x - 1 = 0$ are in $G.P.$,then the roots are

If the first term of an infinite geometric series is $1$ and each term is equal to the sum of all the terms that follow it,then what is its fourth term?

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 $4^{th}$,$7^{th}$,and $10^{th}$ terms of a Geometric Progression $(GP)$ are $a, b,$ and $c$ respectively,then:

The first term of an infinite geometric progression is $x$ and its sum is $5$. Then:

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