Question

Which of the following points is on the graph of y = log1/2x?

(1, 1/2)
(1/2, 1)
(0, 1)
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Answer 1

Answer:

(1/2,1) is on the graph of $y=\log_{1/2}x$

B is correct.

Step-by-step explanation:

Given: $y=\log_{1/2}x$

We are given a log function whose base 1/2.

Log property:

$\log_aa=1$

If base and mantissa is same then their value is 1

We need to choose correct point from the options.

Option 1: (1,1/2)

$y=\log_{1/2}1 = 0$

$\dfrac{1}{2}\neq 1$

False

Option 2: (1/2,1)

$y=\log_{1/2}(1/2) = 1$

$1= 1$

True

Option 3:

Log is not defined for x=0.

Hence, (1/2,1) is on the graph of $y=\log_{1/2}x$

Answer 2

Answer: Hello mate!

here we have the function log₀.₅(x)

and we want to see which points are in the graph of this function.

The options are  

(1, 1/2)

(1/2, 1)

(0, 1)  

first: y = log₀.₅(x) = ln(x)/ln(1/2)

when x = 1/2, the function y = ln(1/2)/ln(1/2) = 1

so the point (1/2, 1) is in the graph of the function.

now, ln(0) is undefined, so the point (0,1) is not in the graph.

ln(1) = 0, so y = ln(0)/ln(1/2) = 0, when x is equal to 1, y is equal to 0, then the point (1, 1/2) is not in the graph.

The only point that lies in the graph is (1/2, 1)