Given:
[tex]P(x)=90-25log_2x[/tex]
Required:
We need to find the value of x when P(x)=80.
Explanation:
[tex]Substitute\text{ P\lparen x\rparen=80 in the equation }P(x)=90-25log_2x.[/tex]
[tex]80=90-25log_2x[/tex]
Solve for x.
[tex]25log_2x=90-80[/tex]
[tex]25log_2x=10[/tex]
Divide both sides by 25.
[tex]\frac{25log_2x}{25}=\frac{10}{25}[/tex]
[tex]log_2x=\frac{2}{5}[/tex][tex]Use\text{ If }log_bx=y\text{ then }b^y=x.\text{ here b=2 and }y=\frac{2}{5}.[/tex][tex]x=2^{\frac{2}{5}}[/tex][tex]x=2^{0.4}[/tex][tex]x=1.3\text{ days.}[/tex]
Final answer:
[tex]x=1.3\text{ days.}[/tex]
See a horizontal line from point 80 on the y axis and mark the intersection point on the graph.
