Question

If $y=lo{g}_{a}x$, and a>1, which of the following statements is incorrect?

• A. If x = 1, y = 0
• B. If x = a , y = 1
• C. If x = -1, y is imaginary (compelx)
• D. If 0 < x < 1, y is always less than 0 and decreases without limit as x approaches zero
• E. All of the above statements are correct

Answer 1

The correct option is E All of the above statements are correct

From the graph of $lo{g}_{a}x$ for different values of $a>0$, we can see that

$lo{g}_{a}1=0$

$lo{g}_{a}a=1$

$x$ cann't be negative.

And for $0<x<1$; $y$ is always less than $0$ and decreases without limit as $x$ approaches zero.