.Number of solutions of equation `2^x + 2^(x-1) + 2^(x-2) = 7^x + 7^(x -1) + 7^(x-2)` is

Options

A. 4
B. 2
C. 1
D. 0

Answer

C

Explanation

`2^(x)+2^(x-1)+2^(x-2)=7^(x)+7^(x-1)+7^(x-2)`,
`rArr2^(x)(1+(1)/(2)+(1)/(4))=7^(x)(1+(1)/(7)+(1)/(49))`
`2^(x)xx(7)/(4)=7^(x)xx(57)/(49)`
`2^(X-2)=7^(x-2)xx(57)/(7)`
`rArr ((7)/(2))^(x-2)=(7)/(57)`
`rArr x-2=log_(7//2)((7)/(57))rArrx=2+log_(7//2)((7)/(57))`
Hence, the given equation has one root.