Number of solutions of `log_4(x-1)=log_2(x-3)` is :

Options

A. 3
B. 1
C. 2
D. 0

Answer

B

Explanation

For the given equation to be valid, we must have
`x-1 gt 0` and `x-3 gt 0 implies x gt 3`. ltbrlt Now,
`log_(4)(x-1)=log_(2)(x-3)`
`implies (1)/(2)log_(2) (x-1)=log_(2)(x-3)`
`implies log_(2)(x-1)=log_(2)(x-3)^(2)`
`implies x-1=(x-3)^(2)`
`implies x^(2)-7x+10=0 implies x=2,5 implies x=5 " "[:' x gt3]`