Question

(1)If a, b, c are three unequal numbers such that a , b, c are in A.P and b - a , c - b , a are in G.P .. , then a :b:c is
(2) if log2, log(2^x - 1 ) and log ( 2^x + 3) are in A.P then x is equal to .

Answer 1

$\huge \pink{Hello!!!}$

(1) Solution :-

By hypothesis

In A.P

(b - a) = (c - b )

And in GP

(c - b )² = a ( b - a)

=> ( b - a )² = a ( b - a)

=> b - a = a (°•° b ≠a)

=> b = 2a and c = 3a

∴ a:b:c = 1 : 2 : 3 Answer

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(2 ) Solution :-

As log2, log(2^x -1) and log (2^x + 3) are in A.P

2log(2^x - 1) = log2 + log(2^x + 3)

=> 2^2x - 4* 2^x - 5 = 0

=> (2^x -5) (2^x + 1) = 0

As ; 2^x cannot be negative, we get 2^x =5

or , x= log₂⁵ Answer

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Answer 2

❤❤Here is your answer ✌ ✌

$\huge {\red {\bold {Answer}}}$

[1]Solution ⬇

By hypothesis 

In Arithmetic progression

=>(b - a) = (c - b ) 

And in GP 

=>(c - b )² = a ( b - a) 

=> ( b - a )² = a ( b - a) 

=> b - a = a (°•° b ≠a) 

=> b = 2a and c = 3a 

∴ a:b:c = 1 : 2 : 3 Answer