EXPLANATION
We need to equal the equation to 75, wich represent the 3/4 of the number of students:
[tex]75=80-35\log _2x[/tex]
Adding +35log_2 x to both sides:
[tex]75+35\log _2x=80[/tex]
Subtracting -75 to both sides:
[tex]35\log _2x=80-75[/tex]
Dividing both sides by 35:
[tex]\log _2x=\frac{5}{35}[/tex]
Simplifying:
[tex]\log _2x=\frac{1}{7}[/tex]
Using the logarithmic definition:
[tex]If\text{ log\_a(b)=c then b=a}^c[/tex][tex]\log _2\mleft(x\mright)=\frac{1}{7}\quad \Rightarrow\quad \: x=\sqrt[7]{2}[/tex]
The solution is:
[tex]x=\sqrt[7]{2}[/tex]
Simplifying:
[tex]x=1.104[/tex]
Plugging in x into the function:
[tex]P(\sqrt[7]{2})=80-35\cdot\log _2(\sqrt[7]{2})[/tex]
[tex]=75[/tex]
The ordered pair is (1.104,75)
