Question

Use the equation and type the ordered-pairs. y = log 3 x {(1/3, a0), (1, a1), (3, a2), (9, a3), (27, a4), (81, a5)

Answer 1

Considering the given equation
`y = log_(3)x\\`

And the ordered pairs in the format
`(x, y)`

I don't know if it is log of base 3 or 10, but I will assume it is 3.

For
`((1)/(3), a_(0) )`

`x=(1)/(3)`

`y=a_(0)`

`y = log_(3)x\\y = log_(3)((1)/(3) )\\y=-\log _3\left(3\right)\\y=-1`

So the ordered pair will be
`((1)/(3), -1 )`

For
`(1, a_(1) )`

`x=1`

`y=a_(1)`

`y = log_(3)x\\y = log_(3)1\\y = log_(3)(1)\\Note: \log _a(1)=0\\y = 0`

So the ordered pair will be
`(1, 0 )`

For
`(3, a_(2) )`

`x=3`

`y=a_(2)`

`y = log_(3)x\\y = log_(3)3\\y = 1`

So the ordered pair will be
`(3, 1 )`

For
`(9, a_(3) )`

`x=9`

`y=a_(3)`

`y = log_(3)x\\y = log_(3)9\\y=2\log _3\left(3\right)\\y=2`

So the ordered pair will be
`(9, 2 )`

For
`(27, a_(4) )`

`x=27`

`y=a_(4)`

`y = log_(3)x\\y = log_(3)27\\y=3\log _3\left(3\right)\\y=3`

So the ordered pair will be
`(27, 3 )`

For
`(81, a_(5) )`

`x=81`

`y=a_(5)`

`y = log_(3)x\\y = log_(3)81\\y=4\log _3\left(3\right)\\y=4`

So the ordered pair will be
`(81, 4 )`