If `log2,log(2^x-1)a n dlog2log(2^x+3)` are in A.P., write the value of `xdot`

Options

A. `5//2`
B. `log_(2)5`
C. `log_(3)5`
D. `log_(5)3`

Answer

B

Explanation

It is given that
`log2,log(2^(x)-1),log(2^(x)+3)` are A.P
`rArr2log(2^(x)-1)=log2+log(2^(x)+3)`
`rArr" "(2^(x)-1)^(2)=2(2^(x)+3)`
`rArr" "(2^(x))^(2)-4(2^(x))-5=0`
`rArr" "(2^(x)-5)(2^(x)+1)=0rArr2^(x)=5rArrx=log_(2)5`