Question

If a > 0, b > 0, c > 0 are in G.P. then in A.P. then the numbers are?

a) log a, log b, log c

b) log (3/a) , log (2/b) , log (1/c)

c) log3 / log a , log2 / log b , log 1/log c

d) 1/a, 1/b, 1/c

e) None of the others

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

The Correct answer is option A

Step-by-step explanation:

• Given a, b, c are in G.P. which means the square of the second term is the product of first term and third term i.e. b2=ac . Apply logarithm to it and solve the logarithm to find which progression are log a, log b, log c in.

Given that the variables a, b, c are in geometric progression.

Find log a, log b, log c are in which progression.

We know that when the numbers or variables are in Geometric Progression, then the square of the 2nd term is equal to the product of the 1st term and 3rd term.

Here a is the 1st term, b is the 2nd term and c is the 3rd term.

This means $b^{2}=ac$

Apply logarithm to the above equation, $b^{2}=ac$

$log(b^{2})=log(ac)$

Where $log(an)=nloga , \\log(ab)=loga+logb$

$log(b^{2})=2log b \ log(ac)\\=log a + log c \ log(b^{2})\\=log(ac)\\=2logb=log a + log c$

When p, q, r are in an Arithmetic progression, then $2q=p+r$

Here

$p=log a,\\q=log b$,$r=logc\\2q=p+r2logb=loga+logc$

Therefore, log a, log b, log c are in Arithmetic Progression.

Reference Link

• https://brainly.in/question/16077886
• https://brainly.in/question/16507884