Home
Class 12
MATHS
If log3 2, log3 (2^x -5) and log3 (2^x-7...

If `log_3 2, log_3 (2^x -5)` and `log_3 (2^x-7/2)` are in `A.P`, determine the value of `x`.

A

2

B

3

C

4

D

`2,3`

Text Solution

Verified by Experts

The correct Answer is:
B
`:. log_(3)2,log_(3)(2^(x)-5)` and `log_(3)(2^(x)-(7)/(2))" are in AP. " " " "……..(i)"`
For defined, `2^(x)-5gt0` and `2^(x)-(7)/(2)gt0`
`:. 2^(x)gt5 " " "…(ii)"`
From Eq.(i),`2,2^(x)-5,2^(x)-(7)/(2)` are in GP. `:." " (2^(x)-5)^(2)=2*(2^(x)-(7)/(2))`
`implies 2^(2x)-12*2^(x)+32=0`
`implies (2^(x)-8)(2^(x)-4)=0`
`:." " 2^(x)=8,4`
`implies 2^(x)=8=2^(3),2^((x) ne4 " " [" from Eq. (ii) "]`.
Promotional Banner

Similar Questions

Explore conceptually related problems

If log_2 log_3 log_4 (x+1) =0, then x is :-

If log ((x+y)/3)=1/2 (log x +log y) then find the value of x/y+y/x

Given log_(10)2 = a and log_(10)3 = b . If 3^(x+2) = 45 , then the value of x in terms of a and b is-

Suppose 3 sin ^(-1) ( log _(2) x ) + cos^(-1) ( log _(2) y) =pi //2 " and " sin^(-1) ( log _(2) x ) + 2 cos^(-1) ( log_(2) y) = 11 pi//6 , then the value of x^(-2) + y^(-2) equals

Suppose that, log_(10) (x-2) + log_(10) y=0 and sqrt(x)+sqrt(y-2)=sqrt(x+y) . Then the value of (x + y) , is

If log_(9)x +log_(4)y = (7)/(2) and log_(9) x - log_(8)y =- (3)/(2) , then x +y equals

If x , y , z are in A.P. , then the value of the determinant are in A.P. , then the value of the determinant |a+2a+3a+2x a+3a+4a+2y a+4a+5a+2z| is a. 1 b. 0 c. 2a d. a

If log_(x)log_(18) (sqrt(2)+sqrt(8)) = (-1)/(2) . Then the value of x .

If log_(y)x +log_(x)y = 7 , then the value of (log_(y)x)^(2) +(log_(x)y)^(2) , is

If a gt 0 and a ne 1, 2 log_(x)a +log_(ax)a +3 log_(a^(2)x) a = 0 , then x =