Question

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

-1/81, 2
0,1
1/9, -1
3, 243
9,1
81,2

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