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If a, b, c are in G.P. and logca, logbc, loga​b are in A.P. then find the common difference of the A.P.?
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If a, b, c are in G.P. and logca, logbc, loga​b are in A.P. then find ...
Solution:

Given, a, b, c are in G.P and logca, logbc, loga​b are in A.P.

Let's assume that the common ratio of the G.P. is r.

So, a, b and c can be written as follows.

a = c/r

b = c

c = cr

Then, the given logarithmic terms can be expressed as:

logca = log(c/r)c = logc - logr

logbc = logc c = logc

loga​b = logb/a = logb - loga = logc - 2logr

We know that logca, logbc, loga​b are in A.P.

So, we can write:

2logc - logr = logc

2logc - 2logr = logc - logr

2(logc - logr) = logc - logr

logc - 2logr = logc - logr

Therefore, the common difference of the A.P. is -logr.

Hence, the answer is -logr.
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If a, b, c are in G.P. and logca, logbc, loga​b are in A.P. then find ...
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If a, b, c are in G.P. and logca, logbc, loga​b are in A.P. then find the common difference of the A.P.?
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If a, b, c are in G.P. and logca, logbc, loga​b are in A.P. then find the common difference of the A.P.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If a, b, c are in G.P. and logca, logbc, loga​b are in A.P. then find the common difference of the A.P.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a, b, c are in G.P. and logca, logbc, loga​b are in A.P. then find the common difference of the A.P.?.
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