Question

what is the domain of x^1/logx

Answer 1

y = x^1/logx

[ we know, 1/log(a base b) = log(b base a) ]

y = x^{ log(e base x )}

[ use, a^log{b base a } = b ]

y = e
hence, function is constant so, it is parallel to X- axis
so , x € R

but here two functions
exponential and logarithm.
for exponential ,x€R : x ≠ 1
and for logarithmic,
x > 0

hence,
x€ (0, 1) U(1 , ∞)

Answer 2

Step-by-step explanation:

y = x^1/logx

[ we know, 1/log(a base b) = log(b base a) ]

y = x^{ log(e base x )}

[ use, a^log{b base a } = b ]

y = e

hence, function is constant so, it is parallel to X- axis

so , x € R

but here two functions

exponential and logarithm.

for exponential ,x€R : x ≠ 1

and for logarithmic,

x > 0

hence,

x€ (0, 1) U(1 , ∞)