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Arithmetic Mean

1. if a, b, c...

Question

1. if a,b,c,d are in ap then log a to base x, log b to base x, log c to base x are in ?

2.the value of (1/sq root27)^2-(log16 base5/ 2log9 base5)

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Solution

Only one question per upload.

Solving the first one

We can say for sure that if log a, log b, log c, are in Arithmetic Progression then, a,b, c are in Geometric Progression

Since log a, log b, log c are in AP

2log b=log a + log c

log(b²)=log(ac)

so b²=ac

Hence they form a Geometric Progression

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