Question

Which answer represents the range of the logarithmic function given below?

Answer 1

Answer:

Option D is correct .i.e., All Real Number

Step-by-step explanation:

Given Logarithmic Function, $F(x)=log\,0.5^x$

First we simply the function,

$F(x)=log\,0.5^x$

F(x) = x × log(0.5)

F(x) = -0.30103x  (by putting value of log(0.5) )

Its clear range of F(x) completely depends on value of x .i.e, Domain of Function

Domain of log function is real Numbers

⇒ Ranges is also the Real Numbers

Therefore, Option D is correct .i.e., All Real Number

Answer 2

Answer:   D) All real numbers

Step-by-step explanation:

F(x) = log (0.5)ˣ

There is no restriction on x, so there is no restriction on y,

therefore y is all real numbers

see attached graph for verification