Question

Which points lie on the graph of f(x) = log9x?

Answer 1

Let

y=f(x)

so
y=log9x

we know that

applying property of logarithms

y= log9x is equal to

$9^{y}=x$ ------> equation 1

so

case 1) (-1/81, 2)

x=-1/81

y=2

substitute the value of y in the equation 1 to obtain the value of x

$9^{2}=81$

81 is not equal to -1/81-------> the point does not belong to the graph

case 2) (0, 1)

x=0

y=1

substitute the value of y in the equation 1 to obtain the value of x

$9^{1}=9$

9 is not equal to 0-------> the point does not belong to the graph

case 3) (1/9, -1)

x=1/9

y=-1

substitute the value of y in the equation 1 to obtain the value of x

$9^{-1}=1/9$

1/9 is equal to 1/9-------> the point belongs to the graph

case 4) (3, 243)

x=3

y=243

substitute the value of y in the equation 1 to obtain the value of x

$9^{243}$

9^{243} is not equal to 3-------> the point does not belong to the graph

case 5) (9, 1)

x=9

y=1

substitute the value of y in the equation 1 to obtain the value of x

$9^{1}= 9$

9 is equal to 9-------> the point belongs to the graph

case 6) (81, 2)

x=81

y=2

substitute the value of y in the equation 1 to obtain the value of x

$9^{2}=81$

81 is equal to 81-------> the point belongs to the graph

Answer 2

Answer:

The other guy is correct but to make it simpler

The answers are:

3, 5, and 6