Question

If log3 2, log3 (2x - 5) and log3 (2x - 7/2) are in arithmetic progression, then the value of x is equal to

Answer 1

For three numbers in arithmetic progression,

2 log3 (2x - 5) = log3 2 + log3 (2x - 7/2)

log3 (2x - 5)2 = log3 (2)(2x - 7/2)

(2x - 5)2 = 2(2x - 7/2)

Let 2x = y

(y - 5)2 = 2(y - 7/2)

y2 + 25 - 10y = 2y - 7

y2 - 12y + 32 = 0

(y - 8)(y - 4) = 0

y = 4 or 8

x = 2 or 3

But, if x= 2 then 2nd term is negative, so x = 3

Answer 2

Answer:

your question is too hard i don't know the answer

Step-by-step explanation:

your question is too hard i don't know the answer