Question

Match the y-coordinate with the given x-coordinate for the equation y = log2x.1.8-12.413.234.105.1/22,

Answer 1

Given:

`y=\text{log}_2x`

Recall that

`\text{If }y=\log _bx\text{ then }b^y=x\text{. Here b=2.}`
`2^y=x`

1. Substitute x=8 in the equation.

`2^y=8`

`2^y=2^3`
`y=3`

The answer for 8 is 3.

2.

Substitute x=4 in the equaiton.

`2^y=4`

`2^y=2^2`
`y=2`

The answer for 4 is 2.

3.

Substitute x=2 in the equaiton.

`2^y=2`
`y=1`

The answer for 2 is 1.

4.

Substitute x=1 in the equaiton.

`2^y=1`

`2^y=2^0`
`y=0`

The answer for 1 is 0.

5.

Substitute x=1/2 in the equaiton.

`2^y=(1)/(2)`

`2^y=(1)/(2)`