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Question: If log<sub>5</sub>2, log<sub>5</sub> (2<sup>x</sup> – 5) and log<sub>5</sub> (2<sup>x</sup> – 7/2) a...

If log52, log5 (2x – 5) and log5 (2x – 7/2) are in A.P., then x is equal to –

A

1/2, 3/2

B

3

C

4, 5

D

8

Answer

3

Explanation

Solution

As log52, log5 (2x – 5), log5(2x – 7/2) are in A.P.,

we get 2 log5(2x – 5) = log52 + log5 (2x – 7/2)

̃ (2x – 5)2 = 2(2x – 7/2)

̃ (2x)2 – 12 (2x) + 32 = 0

̃ (2x – 4) (2x – 8) = 0

̃ 2x = 22, 23 ̃ x = 2, 3.

Clearly, x ¹ 2. Therefore x = 3.