If `f(x)=log_(x^(2))25 " and " g(x)=log_(x)5`, then f(x)=g(x) holds, now find the interval for x.

Options

A. R
B. `{x:0 lt x lt oo, xne 1}`
C. `phi`
D. None of these

Answer

B

Explanation

We have
`f(x)=log_(x^(2)) 25=log_(x^(2)) 5^(2)=(2)/(2)log_(x)5=log_(x)5=g(x)`
for all x in their common domain.
Now, `D_(1)="Domain of f"=R-{0,-1,1}`
`and D_(2)="Domain of g"={x:x gt 0, x ne 1}`
`therefore D_(1) nn D_(2)={x:x gt 0, x ne 1}`
`"Thus", f(x)=g(x)"for all" x in {x:x gt 0, xne1}`