Question

Please read the following and locate the point on the graph that conveys this information

Answer 1

Step-by-step explanation

We need to equal the equation to 75, wich represent the 3/4 of the number of students:

`75=80-35\log _2x`

Adding +35log_2 x to both sides:

`75+35\log _2x=80`

Subtracting -75 to both sides:

`35\log _2x=80-75`

Dividing both sides by 35:

`\log _2x=(5)/(35)`

Simplifying:

`\log _2x=(1)/(7)`

Using the logarithmic definition:

`If\text{ log\_a(b)=c then b=a}^c`
`\log _2\mleft(x\mright)=(1)/(7)\quad \Rightarrow\quad \: x=\sqrt[7]{2}`

The solution is:

`x=\sqrt[7]{2}`

Simplifying:

`x=1.104`

Plugging in x into the function:

`P(\sqrt[7]{2})=80-35\cdot\log _2(\sqrt[7]{2})`

`=75`

The ordered pair is (1.104,75)